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{{more footnotes|date=September 2012}} | |||
{| class="infobox" style="width: 22em" | |||
! colspan="3" style="font-size: 125%; text-align: center;" | LCP array | |||
|- | |||
! [[List of data structures|Type]] | |||
| colspan="2" | [[Array data structure|Array]] | |||
|- | |||
! Invented by | |||
{{!}} colspan="2" {{!}} {{harvtxt|Manber|Myers|1990}} | |||
|- | |||
! colspan="3" class="navbox-abovebelow" | [[Time complexity]] and [[space complexity]]<br />in [[big O notation]] | |||
|- | |||
| | |||
| Average | |||
| Worst case | |||
|- | |||
! Space | |||
| <math>\mathcal{O}(n)</math> | |||
| <math>\mathcal{O}(n)</math> | |||
|- | |||
! Construction | |||
| <math>\mathcal{O}(n)</math> | |||
| <math>\mathcal{O}(n)</math> | |||
|} | |||
In [[computer science]], the '''longest common prefix array''' (LCP [[Array data structure|array]]) is an auxiliary [[data structure]] to the [[suffix array]]. It stores the lengths of the longest common prefixes between pairs of consecutive [[Suffix (computer science)|suffixes]] in the sorted suffix array. | |||
Augmenting the suffix array with the LCP array allows to efficiently simulate top-down and bottom-up [[Tree traversal|traversals]] of the [[suffix tree]],{{sfn|Kasai|Lee|Arimura|Arikawa|2001}}{{sfn|Abouelhoda|Kurtz|Ohlebusch|2004}} speeds up pattern matching on the suffix array{{sfn|Manber|Myers|1993}} and is a prerequisite for compressed suffix trees.{{sfn|Ohlebusch|Fischer|Gog|2010}} | |||
== History == | |||
The LCP array was introduced by [[Udi Manber]] and [[Gene Myers]] alongside the suffix array in order to improve the running time of their string search algorithm.{{sfn|Manber|Myers|1993}} | |||
== Definition == | |||
Let <math>A</math> be the suffix array of the string <math>S=s_1,s_2,...s_n$</math> and let <math>\operatorname{lcp}(v,w)</math> denote the length of the longest common prefix between two strings <math>v</math> and <math>w</math>. Let further denote <math>S[i,j]</math> the substring of <math>S</math> ranging from <math>i</math> to <math>j</math>. | |||
Then the LCP array <math>H[1,n]</math> is an integer array of size <math>n</math> such that <math>H[1]</math> is undefined and <math>H[i]=\operatorname{lcp}(S[A[i-1],n],S[A[i],n])</math> for every <math>1<i\leq n</math>. Thus <math>H[i]</math> stores the length of longest common prefix of the [[Lexicographical order|lexicographically]] <math>i</math>'th smallest suffix and its predecessor in the suffix array. | |||
== Example == | |||
Consider the string <math>S=banana$</math>: | |||
{| class="wikitable" | |||
|- | |||
! {{left header}} | i | |||
| 1 || 2 || 3 || 4 || 5 || 6 || 7 | |||
|- | |||
! {{left header}} | S[i] | |||
| b || a || n || a || n || a || $ | |||
|} | |||
and its corresponding suffix array <math>A</math> : | |||
{| class="wikitable" | |||
! {{left header}} | i | |||
| 1 || 2 || 3 || 4 || 5 || 6 || 7 | |||
|- | |||
! {{left header}} | A[i] | |||
| 7 || 6 || 4 || 2 || 1 || 5 || 3 | |||
|} | |||
Complete suffix array with suffixes itself : | |||
{| class="wikitable" | |||
! {{left header}} | i | |||
| 1 || 2 || 3 || 4 || 5 || 6 || 7 | |||
|- | |||
! {{left header}} | A[i] | |||
| 7 || 6 || 4 || 2 || 1 || 5 || 3 | |||
|- | |||
! {{left header}} | 1 | |||
| $ || a || a || a || b || n || n | |||
|- | |||
! {{left header}} | 2 | |||
| || $ || n || n || a || a || a | |||
|- | |||
! {{left header}} | 3 | |||
| || || a || a || n || $ || n | |||
|- | |||
! {{left header}} | 4 | |||
| || || $ || n || a || || a | |||
|- | |||
! {{left header}} | 5 | |||
| || || || a || n || || $ | |||
|- | |||
! {{left header}} | 6 | |||
| || || || $ || a || || | |||
|- | |||
! {{left header}} | 7 | |||
| || || || || $ || || | |||
|} | |||
Then the LCP array <math>H</math> is constructed by comparing lexicographically consecutive suffixes to determine their longest common prefix: | |||
{| class="wikitable" | |||
|- | |||
! {{left header}} | i | |||
| 1 || 2 || 3 || 4 || 5 || 6 || 7 | |||
|- | |||
! {{left header}} | H[i] | |||
| <math>\bot</math> || 0 || 1 || 3 || 0 || 0 || 2 | |||
|} | |||
So, for example, <math>H[4]=3</math> is the length of the longest common prefix <math>ana</math> shared by the suffixes <math> A[3]=S[4,7]=ana$</math> and <math>A[4]=S[2,7]=anana$</math>. Note that <math>H[1]=\bot</math>, since there is no lexicographically smaller suffix. | |||
== Efficient Construction Algorithms == | |||
LCP array construction algorithms can be divided into two different | |||
categories: algorithms that compute the LCP array as a byproduct to the suffix | |||
array and algorithms that use an already constructed suffix array in order to | |||
compute the LCP values. | |||
{{harvtxt|Manber|Myers|1993}} provide an algorithm to compute the LCP array alongside the suffix array | |||
in <math>O(n \log n)</math> time. {{harvtxt|Kärkkäinen|Sanders|2003}} show that it is also possible to modify their | |||
<math>O(n)</math> time algorithm such that it computes the LCP array as well. | |||
{{harvtxt|Kasai|Lee|Arimura|Arikawa|2001}} present the first <math>O(n)</math> time algorithm (FLAAP) that computes the LCP | |||
array given the text and the suffix array. | |||
Assuming that each text symbol takes | |||
one byte and each entry of the suffix or LCP array takes 4 bytes, the major drawback of their | |||
algorithm is a large space occupancy of <math>13n</math> bytes, while the | |||
original output (text, suffix array, LCP array) only occupies <math>9n</math> | |||
bytes. Therefore {{harvtxt|Manzini|2004}} created a refined version of the algorithm of {{harvtxt|Kasai|Lee|Arimura|Arikawa|2001}} (lcp9) and reduced the | |||
space occupancy to <math>9n</math> bytes. {{harvtxt|Kärkkäinen|Manzini|Puglisi|2009}} provide another refinement of | |||
Kasai's algorithm (<math>\Phi</math>-algorithm) that improves the running | |||
time. Rather than the actual LCP array, this algorithm builds the ''permuted'' | |||
LCP (PLCP) array, in which the values appear in text order rather than lexicographical order. | |||
{{harvtxt|Gog|Ohlebusch|2011}} provide two algorithms that although being theoretically slow | |||
(<math>O(n^2)</math>) were faster than the above mentioned algorithms in | |||
practice. | |||
As of 2012, the currently fastest linear-time LCP array construction algorithm is due to {{harvtxt|Fischer|2011}}, | |||
which in turn is based on one of the fastest suffix array construction algorithms by {{harvtxt|Nong|Zhang|Chan|2009}}. | |||
== Applications == | |||
As noted by {{harvtxt|Abouelhoda|Kurtz|Ohlebusch|2004}} several string processing problems can be solved by the following kinds of [[tree traversal]]s: | |||
* bottom-up traversal of the complete suffix tree | |||
* top-down traversal of a subtree of the suffix tree | |||
* suffix tree traversal using the suffix links. | |||
{{harvtxt|Kasai|Lee|Arimura|Arikawa|2001}} show how to simulate a bottom-up traversal of the [[suffix tree]] using only the [[suffix array]] and LCP array. {{harvtxt|Abouelhoda|Kurtz|Ohlebusch|2004}} enhance the suffix array with the LCP array and additional data structures and describe how this ''enhanced suffix array'' can be used to simulate ''all three kinds'' of suffix tree traversals. {{harvtxt|Fischer|Heun|2007}} reduce the space requirements of the enhanced suffix array by preprocessing the LCP array for [[Range Minimum Query|range minimum queries]]. Thus, ''every'' problem that can be solved by suffix tree algorithms can also be solved using the ''enhanced suffix array''.{{sfn|Abouelhoda|Kurtz|Ohlebusch|2004}} | |||
Deciding if a pattern <math>P</math> of length <math>m</math> is a substring of a string <math>S</math> of length <math>n</math> takes <math> O(m \log n)</math> time if only the suffix array is used. By additionally using the LCP information, this bound can be improved to <math>O(m + \log n)</math> time.{{sfn|Manber|Myers|1993}} {{harvtxt|Abouelhoda|Kurtz|Ohlebusch|2004}} show how to improve this running time even further to achieve optimal <math>O(m)</math> time. Thus, using suffix array and LCP array information, the decision query can be answered as fast as using the [[suffix tree]]. | |||
The LCP array is also an essential part of compressed suffix trees which provide full suffix tree functionality like suffix links and [[lowest common ancestor]] queries.{{sfn|Sadakane|2007}}{{sfn|Fischer|Mäkinen|Navarro|2009}} Furthermore it can be used together with the suffix array to compute the Lempel-Ziv [[LZ77 and LZ78|LZ77]] factorization in <math>O(n)</math> time. {{sfn|Abouelhoda|Kurtz|Ohlebusch|2004}}{{sfn|Crochemore|Ilie|2008}}{{sfn|Crochemore|Ilie|Smyth|2008}}{{sfn|Chen|Puglisi|Smyth|2008}} | |||
The [[longest repeated substring problem]] for a string <math>S</math> of length <math>n</math> can be solved in <math>\Theta(n)</math> time using both the suffix array <math>A</math> and the LCP array. It is sufficient to perform a linear scan through the LCP array in order to find its maximum value <math>v_{max}</math> and the corresponding index <math>i</math> where <math>v_{max}</math> is stored. The longest substring that occurs at least twice is then given by <math>S[A[i],A[i]+v_{max}-1]</math>. | |||
The remainder of this section explains two applications of the LCP array in more detail: How the suffix array and the LCP array of a string can be used to construct the corresponding suffix tree and how it is possible to answer LCP queries for arbitrary suffixes using range minimum queries on the LCP array. | |||
=== Suffix Tree Construction === | |||
Given the suffix array <math>A</math> and the LCP array <math>H</math> of a string <math>S=s_1,s_2,...s_n$</math> of length <math>n+1</math>, its suffix tree <math>ST</math> can be constructed in <math>O(n)</math> time based on the following idea: Start with the partial suffix tree for the lexicographically smallest suffix and repeatedly insert the other suffixes in the order given by the suffix array. | |||
Let <math>ST_{i}</math> be the partial suffix tree for <math>0\leq i \leq n</math>. Further let <math>d(v)</math> be the length of the concatenation of all path labels from the root of <math>ST_i</math> to node <math>v</math>. | |||
[[File:Constructing the suffix tree of banana based on the suffix array and the LCP array - Case 1.pdf|thumb|400px|Case 1 (<math>d(v)=H[i+1]</math>): Suppose the suffixes <math>a$</math>, <math>ana$</math>, <math>anana$</math> and <math>banana$</math> of the string <math>S=banana$</math> are already added to the suffix tree. Then the suffix <math>na$</math> is added to the tree as shown in the picture. The ''rightmost'' path is highlighted in red.]] | |||
Start with <math>S_0</math>, the tree consisting only of the root. To insert <math>A[i+1]</math> into <math>ST_i</math>, walk up the ''rightmost'' path beginning at the recently inserted leaf <math>A[i]</math> to the root, until the deepest node <math>v</math> with <math>d(v) \leq H[i+1]</math> is reached. | |||
We need to distinguish two cases: | |||
* <math>d(v)=H[i+1]</math>: This means that the concatenation of the labels on the root-to-<math>v</math> path equals the longest common prefix of suffixes <math>A[i]</math> and <math>A[i+1]</math>. <br /> In this case, insert <math>A[i+1]</math> as a new leaf <math>x</math> of node <math>v</math> and label the edge <math>(v,x)</math> with <math>S[A[i+1]+H[i+1],n]</math>. Thus the edge label consists of the remaining characters of suffix <math>A[i+1]</math> that are not already represented by the concatenation of the labels of the root-to-<math>v</math> path. <br />This creates the partial suffix tree <math>ST_{i+1}</math>. [[File:Constructing the suffix tree of banana based on the suffix array and the LCP array - Case 2.pdf|thumb|400px|Case 2 (<math>d(v) < H[i+1]</math>): In order to add suffix <math>nana$</math>, the edge to the previously inserted suffix <math>na$</math> has to be split up. The new edge to the new internal node is labeled with the longest common prefix of the suffixes <math>na$</math> and <math>nana$</math>. The edges connecting the two leafs are labeled with the ''remaining'' suffix characters that are not part of the prefix.]] | |||
*<math>d(v) < H[i+1]</math>: This means that the concatenation of the labels on the root-to-<math>v</math> path displays less characters than the longest common prefix of suffixes <math>A[i]</math> and <math>A[i+1]</math> and the ''missing'' characters are contained in the edge label of <math>v</math>'s ''rightmost'' edge. Therefore we have to ''split up'' that edge as follows: <br />Let <math>w</math> be the child of <math>v</math> on <math>ST_i</math>'s rightmost path. | |||
# Delete the edge <math>(v,w)</math>. | |||
# Add a new internal node <math>y</math> and a new edge <math>(v,y)</math> with label <math>S[A[i]+d(v),A[i]+H[i+1]-1]</math>. The new label consists of the ''missing'' characters of the longest common prefix of <math>A[i]</math> and <math>A[i+1]</math>. Thus, the concatenation of the labels of the root-to-<math>y</math> path now displays the longest common prefix of <math>A[i]</math> and <math>A[i+1]</math>. | |||
# Connect <math>w</math> to the newly created internal node <math>y</math> by an edge <math>(y,w)</math> that is labeled <math>S[A[i]+H[i+1],A[i]+d(w)-1]</math>. The new label consists of the ''remaining'' characters of the deleted edge <math>(v,w)</math> that were not used as the label of edge <math>(v,y)</math>. | |||
# Add <math>A[i+1]</math> as a new leaf <math>x</math> and connect it to the new internal node <math>y</math> by an edge <math>(y,x)</math> that is labeled <math>S[A[i+1]+H[i+1],n]</math>. Thus the edge label consists of the remaining characters of suffix <math>A[i+1]</math> that are not already represented by the concatenation of the labels of the root-to-<math>v</math> path. | |||
# This creates the partial suffix tree <math>ST_{i+1}</math>. | |||
A simple amortization argument shows that the running time of this algorithm is bounded by <math>O(n)</math>: | |||
The nodes that are traversed in step <math>i</math> by walking up the ''rightmost'' path of <math>ST_i</math> (apart from the last node <math>v</math>) are removed from the ''rightmost'' path, when <math>A[i+1]</math> is added to the tree as a new leaf. These nodes will never be traversed again for all subsequent steps <math>j>i</math>. Therefore, at most <math>2n</math> nodes will be traversed in total. | |||
=== LCP queries for arbitrary suffixes === | |||
The LCP array <math>H</math> only contains the length of the longest common prefix of every pair of consecutive suffixes in the suffix array <math>A</math>. However, with the help of the inverse suffix array <math>A^{-1}</math> (<math> A[i]= j \Leftrightarrow A^{-1}[j]= i </math>, i.e. the suffix <math>S[j,n]</math> that starts at position <math>j</math> in <math>S</math> is stored in position <math>A^{-1}[j]</math> in <math>A</math>) and constant-time [[Range Minimum Query|range minimum queries]] on <math>H</math>, it is possible to determine the length of the longest common prefix of arbitrary suffixes in <math>O(1)</math> time. | |||
Because of the lexicographic order of the suffix array, every common prefix of the suffixes <math>S[i,n]</math> and <math>S[j,n]</math> has to be a common prefix of all suffixes between <math>i</math>'s position in the suffix array <math> A^{-1}[i]</math> and <math>j</math>'s position in the suffix array <math> A^{-1}[j] </math>. Therefore the length of the longest prefix that is shared by ''all'' of these suffixes is the minimum value in the interval <math>H[A^{-1}[i]+1,A^{-1}[j]]</math>. This value can be found in constant time if <math>H</math> is preprocessed for range minimum queries. | |||
Thus given a string <math>S</math> of length <math>n</math> and two arbitrary positions <math>i,j</math> in the string <math>S</math> with <math> A^{-1}[i] < A^{-1}[j] </math>, the length of the longest common prefix of the suffixes <math>S[i,n]</math> and <math>S[j,n]</math> can be computed as follows: <math>\operatorname{LCP}(i,j)=H[\operatorname{RMQ}_H(A^{-1}[i]+1,A^{-1}[j])]</math>. | |||
==Notes== | |||
{{Reflist}} | |||
==References== | |||
*{{cite journal| doi=10.1016/S1570-8667(03)00065-0 |ref=harv| title=Replacing suffix trees with enhanced suffix arrays| year=2004| last1=Abouelhoda| first1=Mohamed Ibrahim| last2=Kurtz| first2=Stefan| last3=Ohlebusch| first3=Enno| journal=Journal of Discrete Algorithms| volume=2| pages=53 }} | |||
*{{cite journal| doi=10.1137/0222058 | ref=harv| title=Suffix Arrays: A New Method for On-Line String Searches| year=1993| last1=Manber| first1=Udi| last2=Myers| first2=Gene| journal=SIAM Journal on Computing| volume=22| issue=5| pages=935}} | |||
*{{cite journal |doi = 10.1007/3-540-48194-X_17 |ref=harv| title = Proceedings of the 12th Annual Symposium on Combinatorial Pattern Matching | year = 2001 | last1 = Kasai | first1 = T. | last2 = Lee | first2 = G. | last3 = Arimura | first3 = H. | last4 = Arikawa | first4 = S. | last5 = Park | first5 = K. | chapter = Linear-Time Longest-Common-Prefix Computation in Suffix Arrays and Its Applications | series = Lecture Notes in Computer Science | volume = 2089 | pages = 181–192 | isbn = 978-3-540-42271-6 | |||
}} | |||
*{{cite journal| doi=10.1007/978-3-642-16321-0_34 |ref=harv| chapter=CST++| title=String Processing and Information Retrieval| series=Lecture Notes in Computer Science| year=2010| last1=Ohlebusch| first1=Enno| last2=Fischer| first2=Johannes| last3=Gog| first3=Simon| isbn=978-3-642-16320-3| volume=6393| pages=322}} | |||
*{{cite journal|ref=harv | |||
| title = Simple linear work suffix array construction | |||
| url = http://dl.acm.org/citation.cfm?id=1759210.1759301 | |||
| year = 2003 | |||
| journal = Proceedings of the 30th international conference on Automata, languages and programming | |||
| pages = 943–955 | |||
| last1 = Kärkkäinen | first1 = Juha | |||
| last2 = Sanders | first2 = Peter | |||
| accessdate = 2012-08-28 }} | |||
* {{cite journal| doi = 10.1007/978-3-642-22300-6_32 |ref=harv| last1 = Fischer | first1 = Johannes | chapter = Inducing the LCP-Array | title = Algorithms and Data Structures | series = Lecture Notes in Computer Science | volume = 6844 | pages = 374–385 | year = 2011 | isbn = 978-3-642-22299-3 }} | |||
*{{cite journal| doi=10.1007/978-3-540-27810-8_32 |ref=harv| chapter=Two Space Saving Tricks for Linear Time LCP Array Computation| title=Algorithm Theory - SWAT 2004| series=Lecture Notes in Computer Science| year=2004| last1=Manzini| first1=Giovanni| isbn=978-3-540-22339-9| volume=3111| pages=372}} | |||
*{{cite journal| doi=10.1007/978-3-642-02441-2_17 |ref=harv| chapter=Permuted Longest-Common-Prefix Array| title=Combinatorial Pattern Matching| series=Lecture Notes in Computer Science| year=2009| last1=Kärkkäinen| first1=Juha| last2=Manzini| first2=Giovanni| last3=Puglisi| first3=Simon J.| isbn=978-3-642-02440-5| volume=5577| pages=181}} | |||
*{{cite journal| doi=10.1007/978-3-540-92182-0_14 |ref=harv| chapter=Space-Time Tradeoffs for Longest-Common-Prefix Array Computation| title=Algorithms and Computation| series=Lecture Notes in Computer Science| year=2008| last1=Puglisi| first1=Simon J.| last2=Turpin| first2=Andrew| isbn=978-3-540-92181-3| volume=5369| pages=124}} | |||
*{{cite journal|ref=harv | |||
| title = Fast and Lightweight LCP-Array Construction Algorithms | |||
| url = http://www.siam.org/proceedings/alenex/2011/alx11_03_gogs.pdf | |||
| year = 2011 | |||
| journal = Proceedings of the Workshop on Algorithm Engineering and Experiments, ALENEX 2011 | |||
| pages = 25–34 | |||
| last1 = Gog | first1 = Simon | |||
| last2 = Ohlebusch | first2 = Enno | |||
| accessdate = 2012-08-28 }} | |||
*{{cite journal| doi=10.1109/DCC.2009.42 | ref=harv| chapter=Linear Suffix Array Construction by Almost Pure Induced-Sorting| title=2009 Data Compression Conference| year=2009| last1=Nong| first1=Ge| last2=Zhang| first2=Sen| last3=Chan| first3=Wai Hong| isbn=978-0-7695-3592-0| pages=193}} | |||
*{{cite journal | doi = 10.1007/978-3-540-74450-4_41 | ref=harv| last1 = Fischer | first1 = Johannes | |||
| last2 = Heun | first2 = Volker | |||
| chapter = A New Succinct Representation of RMQ-Information and Improvements in the Enhanced Suffix Array | |||
| title = Combinatorics, Algorithms, Probabilistic and Experimental Methodologies | |||
| series = Lecture Notes in Computer Science | |||
| volume = 4614 | |||
| pages = 459 | |||
| year = 2007 | |||
| isbn = 978-3-540-74449-8 | |||
}} | |||
*{{Cite journal | doi = 10.1007/s11786-007-0024-4 | ref= harv | last1 = Chen | first1 = G. | last2 = Puglisi | first2 = S. J. | last3 = Smyth | first3 = W. F. | title = Lempel–Ziv Factorization Using Less Time & Space | journal = Mathematics in Computer Science | volume = 1 | issue = 4 | pages = 605 | year = 2008 }} | |||
*{{Cite journal | doi = 10.1016/j.ipl.2007.10.006 | ref=harv | last1 = Crochemore | first1 = M. | last2 = Ilie | first2 = L. | title = Computing Longest Previous Factor in linear time and applications | journal = Information Processing Letters | volume = 106 | issue = 2 | pages = 75 | year = 2008 }} | |||
*{{Cite journal | doi = 10.1109/DCC.2008.36 | ref=harv | last1 = Crochemore | first1 = M. | last2 = Ilie | first2 = L. | last3 = Smyth | first3 = W. F. | chapter = A Simple Algorithm for Computing the Lempel Ziv Factorization | title = Data Compression Conference (dcc 2008) | pages = 482 | year = 2008 | isbn = 978-0-7695-3121-2 }} | |||
*{{Cite journal| doi = 10.1007/s00224-006-1198-x |ref=harv| last1 = Sadakane | first1 = K. | title = Compressed Suffix Trees with Full Functionality | journal = Theory of Computing Systems | volume = 41 | issue = 4 | pages = 589–607 | year = 2007 }} | |||
*{{Cite journal | doi = 10.1016/j.tcs.2009.09.012 | rev=harv | last1 = Fischer | first1 = Johannes | last2 = Mäkinen | first2 = Veli | last3 = Navarro | first3 = Gonzalo | title = Faster entropy-bounded compressed suffix trees | journal = Theoretical Computer Science | volume = 410 | issue = 51 | pages = 5354 | year = 2009 }} | |||
== External links == | |||
*[https://github.com/elventear/sais-lite-lcp Mirror of the ad-hoc-implementation of the code described in {{harvtxt|Fischer|2011}}] | |||
*[https://github.com/simongog/sdsl/ SDSL: Succinct Data Structure Library - Provides various LCP array implementations, Range Minimum Query (RMQ) support structures and many more succinct data structures ] | |||
*[https://github.com/carrotsearch/jsuffixarrays/blob/master/src/main/java/org/jsuffixarrays/Traversals.java Bottom-up suffix tree traversal emulated using suffix array and LCP array (Java)] | |||
*[http://code.google.com/p/text-indexing/ Text-Indexing project] (linear-time construction of suffix trees, suffix arrays, LCP array and Burrows-Wheeler Transform) | |||
[[Category:Arrays]] | |||
[[Category:Substring indices]] | |||
[[Category:String data structures]] |
Latest revision as of 22:58, 10 April 2013
LCP array | ||
---|---|---|
Type | Array | |
Invented by | Template:Harvtxt | |
Time complexity and space complexity in big O notation | ||
Average | Worst case | |
Space | ||
Construction |
In computer science, the longest common prefix array (LCP array) is an auxiliary data structure to the suffix array. It stores the lengths of the longest common prefixes between pairs of consecutive suffixes in the sorted suffix array.
Augmenting the suffix array with the LCP array allows to efficiently simulate top-down and bottom-up traversals of the suffix tree,Template:SfnTemplate:Sfn speeds up pattern matching on the suffix arrayTemplate:Sfn and is a prerequisite for compressed suffix trees.Template:Sfn
History
The LCP array was introduced by Udi Manber and Gene Myers alongside the suffix array in order to improve the running time of their string search algorithm.Template:Sfn
Definition
Let be the suffix array of the string and let denote the length of the longest common prefix between two strings and . Let further denote the substring of ranging from to .
Then the LCP array is an integer array of size such that is undefined and for every . Thus stores the length of longest common prefix of the lexicographically 'th smallest suffix and its predecessor in the suffix array.
Example
Template:Left header | i | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|
Template:Left header | S[i] | b | a | n | a | n | a | $ |
and its corresponding suffix array :
Template:Left header | i | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|
Template:Left header | A[i] | 7 | 6 | 4 | 2 | 1 | 5 | 3 |
Complete suffix array with suffixes itself :
Template:Left header | i | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|
Template:Left header | A[i] | 7 | 6 | 4 | 2 | 1 | 5 | 3 |
Template:Left header | 1 | $ | a | a | a | b | n | n |
Template:Left header | 2 | $ | n | n | a | a | a | |
Template:Left header | 3 | a | a | n | $ | n | ||
Template:Left header | 4 | $ | n | a | a | |||
Template:Left header | 5 | a | n | $ | ||||
Template:Left header | 6 | $ | a | |||||
Template:Left header | 7 | $ |
Then the LCP array is constructed by comparing lexicographically consecutive suffixes to determine their longest common prefix:
Template:Left header | i | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|
Template:Left header | H[i] | 0 | 1 | 3 | 0 | 0 | 2 |
So, for example, is the length of the longest common prefix shared by the suffixes and . Note that , since there is no lexicographically smaller suffix.
Efficient Construction Algorithms
LCP array construction algorithms can be divided into two different categories: algorithms that compute the LCP array as a byproduct to the suffix array and algorithms that use an already constructed suffix array in order to compute the LCP values.
Template:Harvtxt provide an algorithm to compute the LCP array alongside the suffix array in time. Template:Harvtxt show that it is also possible to modify their time algorithm such that it computes the LCP array as well. Template:Harvtxt present the first time algorithm (FLAAP) that computes the LCP array given the text and the suffix array.
Assuming that each text symbol takes one byte and each entry of the suffix or LCP array takes 4 bytes, the major drawback of their algorithm is a large space occupancy of bytes, while the original output (text, suffix array, LCP array) only occupies bytes. Therefore Template:Harvtxt created a refined version of the algorithm of Template:Harvtxt (lcp9) and reduced the space occupancy to bytes. Template:Harvtxt provide another refinement of Kasai's algorithm (-algorithm) that improves the running time. Rather than the actual LCP array, this algorithm builds the permuted LCP (PLCP) array, in which the values appear in text order rather than lexicographical order.
Template:Harvtxt provide two algorithms that although being theoretically slow () were faster than the above mentioned algorithms in practice.
As of 2012, the currently fastest linear-time LCP array construction algorithm is due to Template:Harvtxt, which in turn is based on one of the fastest suffix array construction algorithms by Template:Harvtxt.
Applications
As noted by Template:Harvtxt several string processing problems can be solved by the following kinds of tree traversals:
- bottom-up traversal of the complete suffix tree
- top-down traversal of a subtree of the suffix tree
- suffix tree traversal using the suffix links.
Template:Harvtxt show how to simulate a bottom-up traversal of the suffix tree using only the suffix array and LCP array. Template:Harvtxt enhance the suffix array with the LCP array and additional data structures and describe how this enhanced suffix array can be used to simulate all three kinds of suffix tree traversals. Template:Harvtxt reduce the space requirements of the enhanced suffix array by preprocessing the LCP array for range minimum queries. Thus, every problem that can be solved by suffix tree algorithms can also be solved using the enhanced suffix array.Template:Sfn
Deciding if a pattern of length is a substring of a string of length takes time if only the suffix array is used. By additionally using the LCP information, this bound can be improved to time.Template:Sfn Template:Harvtxt show how to improve this running time even further to achieve optimal time. Thus, using suffix array and LCP array information, the decision query can be answered as fast as using the suffix tree.
The LCP array is also an essential part of compressed suffix trees which provide full suffix tree functionality like suffix links and lowest common ancestor queries.Template:SfnTemplate:Sfn Furthermore it can be used together with the suffix array to compute the Lempel-Ziv LZ77 factorization in time. Template:SfnTemplate:SfnTemplate:SfnTemplate:Sfn
The longest repeated substring problem for a string of length can be solved in time using both the suffix array and the LCP array. It is sufficient to perform a linear scan through the LCP array in order to find its maximum value and the corresponding index where is stored. The longest substring that occurs at least twice is then given by .
The remainder of this section explains two applications of the LCP array in more detail: How the suffix array and the LCP array of a string can be used to construct the corresponding suffix tree and how it is possible to answer LCP queries for arbitrary suffixes using range minimum queries on the LCP array.
Suffix Tree Construction
Given the suffix array and the LCP array of a string of length , its suffix tree can be constructed in time based on the following idea: Start with the partial suffix tree for the lexicographically smallest suffix and repeatedly insert the other suffixes in the order given by the suffix array.
Let be the partial suffix tree for . Further let be the length of the concatenation of all path labels from the root of to node .
Start with , the tree consisting only of the root. To insert into , walk up the rightmost path beginning at the recently inserted leaf to the root, until the deepest node with is reached.
We need to distinguish two cases:
- : This means that the concatenation of the labels on the root-to- path equals the longest common prefix of suffixes and .
In this case, insert as a new leaf of node and label the edge with . Thus the edge label consists of the remaining characters of suffix that are not already represented by the concatenation of the labels of the root-to- path.
This creates the partial suffix tree .
- : This means that the concatenation of the labels on the root-to- path displays less characters than the longest common prefix of suffixes and and the missing characters are contained in the edge label of 's rightmost edge. Therefore we have to split up that edge as follows:
Let be the child of on 's rightmost path.
- Delete the edge .
- Add a new internal node and a new edge with label . The new label consists of the missing characters of the longest common prefix of and . Thus, the concatenation of the labels of the root-to- path now displays the longest common prefix of and .
- Connect to the newly created internal node by an edge that is labeled . The new label consists of the remaining characters of the deleted edge that were not used as the label of edge .
- Add as a new leaf and connect it to the new internal node by an edge that is labeled . Thus the edge label consists of the remaining characters of suffix that are not already represented by the concatenation of the labels of the root-to- path.
- This creates the partial suffix tree .
A simple amortization argument shows that the running time of this algorithm is bounded by :
The nodes that are traversed in step by walking up the rightmost path of (apart from the last node ) are removed from the rightmost path, when is added to the tree as a new leaf. These nodes will never be traversed again for all subsequent steps . Therefore, at most nodes will be traversed in total.
LCP queries for arbitrary suffixes
The LCP array only contains the length of the longest common prefix of every pair of consecutive suffixes in the suffix array . However, with the help of the inverse suffix array (, i.e. the suffix that starts at position in is stored in position in ) and constant-time range minimum queries on , it is possible to determine the length of the longest common prefix of arbitrary suffixes in time.
Because of the lexicographic order of the suffix array, every common prefix of the suffixes and has to be a common prefix of all suffixes between 's position in the suffix array and 's position in the suffix array . Therefore the length of the longest prefix that is shared by all of these suffixes is the minimum value in the interval . This value can be found in constant time if is preprocessed for range minimum queries.
Thus given a string of length and two arbitrary positions in the string with , the length of the longest common prefix of the suffixes and can be computed as follows: .
Notes
43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.
References
- One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang - One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang - One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang - One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang - One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang - One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang - One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang - One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang - One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang - One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang - One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang - One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang - One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang - One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang - One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang - One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang - One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
External links
- Mirror of the ad-hoc-implementation of the code described in Template:Harvtxt
- SDSL: Succinct Data Structure Library - Provides various LCP array implementations, Range Minimum Query (RMQ) support structures and many more succinct data structures
- Bottom-up suffix tree traversal emulated using suffix array and LCP array (Java)
- Text-Indexing project (linear-time construction of suffix trees, suffix arrays, LCP array and Burrows-Wheeler Transform)