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{{Infobox Algorithm | |||
|class=[[Sorting algorithm]] | |||
|image=[[File:Sorting shellsort anim.gif|Step-by-step visualisation of Shellsort]]<br/><small>Shellsort with gaps 23, 10, 4, 1 in action.</small> | |||
|data=[[Array data structure|Array]] | |||
|time=depends on gap sequence | |||
|best-time=depends on gap sequence | |||
|average-time=depends on gap sequence | |||
|space=О(n) total, O(1) auxiliary | |||
|optimal=No | |||
}} | |||
'''Shellsort''', also known as '''Shell sort''' or '''Shell's method''', is an in-place [[comparison sort]]. It generalizes an exchanging sort, such as [[insertion sort|insertion]] or [[bubble sort|bubble]] sort, by starting the comparison and exchange of elements with elements that are far apart before finishing with neighboring elements. Starting with far apart elements can move some out-of-place elements into position faster than a simple nearest neighbor exchange. [[Donald Shell]] published the first version of this sort in 1959.<ref name="Shell">{{Cite journal | |||
|url=http://penguin.ewu.edu/cscd300/Topic/AdvSorting/p30-shell.pdf | |||
|last=Shell | |||
|first=D.L. | |||
|title=A High-Speed Sorting Procedure | |||
|journal=Communications of the ACM | |||
|volume=2 | |||
|issue=7 | |||
|year=1959 | |||
|pages=30–32 | |||
|doi=10.1145/368370.368387}}</ref><ref>Some older textbooks and references call this the "Shell-Metzner" sort after [[Marlene Metzner Norton]], but according to Metzner, "I had nothing to do with the sort, and my name should never have been attached to it." See {{Cite web | |||
|title=Shell sort | |||
|publisher=National Institute of Standards and Technology | |||
|url=http://www.nist.gov/dads/HTML/shellsort.html | |||
|accessdate=2007-07-17 }}</ref> The running time of Shellsort is heavily dependent on the gap sequence it uses. For many practical variants, determining their [[time complexity]] remains an [[open problem]]. | |||
== Description == | |||
Shellsort is a generalization of [[insertion sort]] that allows the exchange of items that are far apart. The idea is to arrange the list of elements so that, starting anywhere, considering every ''h''th element gives a sorted list. Such a list is said to be ''h''-sorted. Equivalently, it can be thought of as ''h'' interleaved lists, each individually sorted.<ref name="Sedgewick">{{Cite book | |||
|last=Sedgewick | |||
|first=Robert | |||
|authorlink=Robert Sedgewick (computer scientist) | |||
|title=Algorithms in C | |||
|edition=3rd | |||
|volume=1 | |||
|publisher=Addison-Wesley | |||
|location= | |||
|year=1998 | |||
|pages=273-281 | |||
|isbn=0-201-31452-5}}</ref> Beginning with large values of ''h'', this rearrangement allows elements to move long distances in the original list, reducing large amounts of disorder quickly, and leaving less work for smaller ''h''-sort steps to do.<ref name="KR">{{Cite book | |||
|last1=Kernighan | |||
|first1=Brian W. | |||
|authorlink1=Brian Kernighan | |||
|last2=Ritchie | |||
|first2=Dennis M. | |||
|authorlink2=Dennis Ritchie | |||
|title=The C Programming Language | |||
|edition=2nd | |||
|publisher=Prentice Hall | |||
|year=1996 | |||
|pages=62 | |||
|isbn=7-302-02412-X}}</ref> If the file is then ''k-sorted'' for some smaller integer ''k'', then the file remains ''h''-sorted. Following this idea for a decreasing sequence of ''h'' values ending in 1 is guaranteed to leave a sorted list in the end.<ref name="Sedgewick"/> | |||
An example run of Shellsort with gaps 5, 3 and 1 is shown below. | |||
<math> | |||
\begin{array}{rcccccccccccc} | |||
&a_1&a_2&a_3&a_4&a_5&a_6&a_7&a_8&a_9&a_{10}&a_{11}&a_{12}\\ | |||
\hbox{input data:} | |||
& 62& 83& 18& 53& 07& 17& 95& 86& 47& 69& 25& 28\\ | |||
\hbox{after 5-sorting:} | |||
& 17& 28& 18& 47& 07& 25& 83& 86& 53& 69& 62& 95\\ | |||
\hbox{after 3-sorting:} | |||
& 17& 07& 18& 47& 28& 25& 69& 62& 53& 83& 86& 95\\ | |||
\hbox{after 1-sorting:} | |||
& 07& 17& 18& 25& 28& 47& 53& 62& 69& 83& 86& 95\\ | |||
\end{array} | |||
</math> | |||
The first pass, 5-sorting, performs insertion sort on separate subarrays (''a''<sub>1</sub>, ''a''<sub>6</sub>, ''a''<sub>11</sub>), (''a''<sub>2</sub>, ''a''<sub>7</sub>, ''a''<sub>12</sub>), (''a''<sub>3</sub>, ''a''<sub>8</sub>), (''a''<sub>4</sub>, ''a''<sub>9</sub>), (''a''<sub>5</sub>, ''a''<sub>10</sub>). For instance, it changes the subarray (''a''<sub>1</sub>, ''a''<sub>6</sub>, ''a''<sub>11</sub>) from (62, 17, 25) to (17, 25, 62). The next pass, 3-sorting, performs insertion sort on the subarrays (''a''<sub>1</sub>, ''a''<sub>4</sub>, ''a''<sub>7</sub>, ''a''<sub>10</sub>), (''a''<sub>2</sub>, ''a''<sub>5</sub>, ''a''<sub>8</sub>, ''a''<sub>11</sub>), (''a''<sub>3</sub>, ''a''<sub>6</sub>, ''a''<sub>9</sub>, ''a''<sub>12</sub>). The last pass, 1-sorting, is an ordinary insertion sort of the entire array (''a''<sub>1</sub>,..., ''a''<sub>12</sub>). | |||
As the example illustrates, the subarrays that Shellsort operates on are initially short; later they are longer but almost ordered. In both cases insertion sort works efficiently. | |||
Shellsort is [[sorting algorithm#Stability|unstable]]: it may change the relative order of elements with equal values. It has "natural" behavior, in that it executes faster when the input is partially sorted. | |||
== Pseudocode == | |||
Using Marcin Ciura's gap sequence, with an inner insertion sort. | |||
''# Sort an array a[0...n-1].'' | |||
gaps = [701, 301, 132, 57, 23, 10, 4, 1] | |||
'''[[foreach]]''' (gap in gaps) | |||
{ | |||
''# Do an insertion sort for each gap size.'' | |||
'''for''' (i = gap; i < n; i += 1) | |||
{ | |||
temp = a[i] | |||
'''for''' (j = i; j >= gap and a[j - gap] > temp; j -= gap) | |||
{ | |||
a[j] = a[j - gap] | |||
} | |||
a[j] = temp | |||
} | |||
} | |||
== Gap sequences == | |||
The question of deciding which gap sequence to use is difficult. Every gap sequence that contains 1 yields a correct sort; however, the properties of thus obtained versions of Shellsort may be very different. | |||
The table below compares most proposed gap sequences published so far. Some of them have decreasing elements that depend on the size of the sorted array (''N''). Others are increasing infinite sequences, whose elements less than ''N'' should be used in reverse order. | |||
:{| class="wikitable" | |||
|- style="background-color: #efefef;" | |||
! General term (''k'' ≥ 1) | |||
! Concrete gaps | |||
! Worst-case<br>time complexity | |||
! Author and year of publication | |||
|---- | |||
| <math>\lfloor N / 2^k \rfloor</math> | |||
| <math>\left\lfloor\frac{N}{2}\right\rfloor, | |||
\left\lfloor\frac{N}{4}\right\rfloor, \ldots, 1</math> | |||
| <math>\Theta(N^2)</math> [when ''N''=2<sup>''p''</sup>] | |||
| [[Donald Shell|Shell]], 1959<ref name="Shell"/> | |||
|---- | |||
| <math>2 \lfloor N / 2^{k+1} \rfloor + 1</math> | |||
| <math>2 \left\lfloor\frac{N}{4}\right\rfloor + 1, \ldots, 3, 1</math> | |||
| <math>\Theta(N^{3/2})</math> | |||
| Frank & Lazarus, 1960<ref>{{Cite journal | |||
|last=Frank | |||
|first=R.M. | |||
|last2=Lazarus | |||
|first2=R.B. | |||
|title=A High-Speed Sorting Procedure | |||
|journal=Communications of the ACM | |||
|volume=3 | |||
|issue=1 | |||
|year=1960 | |||
|pages=20–22 | |||
|doi=10.1145/366947.366957}}</ref> | |||
|---- | |||
| <math>2^k - 1</math> | |||
| <math>1, 3, 7, 15, 31, 63, \ldots</math> | |||
| <math>\Theta(N^{3/2})</math> | |||
| Hibbard, 1963<ref>{{Cite journal | |||
|last=Hibbard | |||
|first=Thomas N. | |||
|title=An Empirical Study of Minimal Storage Sorting | |||
|journal=Communications of the ACM | |||
|volume=6 | |||
|issue=5 | |||
|year=1963 | |||
|pages=206–213 | |||
|doi=10.1145/366552.366557}}</ref> | |||
|---- | |||
| <math>2^k + 1</math>, prefixed with 1 | |||
| <math>1, 3, 5, 9, 17, 33, 65, \ldots</math> | |||
| <math>\Theta(N^{3/2})</math> | |||
| Papernov & Stasevich, 1965<ref>{{Cite journal | |||
|url=http://www.mathnet.ru/links/83f0a81df1ec06f76d3683c6cab7d143/ppi751.pdf | |||
|last=Papernov | |||
|first=A.A. | |||
|last2=Stasevich | |||
|first2=G.V. | |||
|title=A Method of Information Sorting in Computer Memories | |||
|journal=Problems of Information Transmission | |||
|volume=1 | |||
|issue=3 | |||
|year=1965 | |||
|pages=63–75}}</ref> | |||
|---- | |||
| successive numbers of the form <math>2^p 3^q</math> | |||
| <math>1, 2, 3, 4, 6, 8, 9, 12, \ldots</math> | |||
| <math>\Theta(N \log^2 N)</math> | |||
| [[Vaughan Ronald Pratt|Pratt]], 1971<ref>{{Cite book | |||
|last=Pratt | |||
|first=Vaughan Ronald | |||
|year=1979 | |||
|publisher=Garland | |||
|title=Shellsort and Sorting Networks (Outstanding Dissertations in the Computer Sciences) | |||
|isbn=0-8240-4406-1}}</ref> | |||
|---- | |||
| <math>(3^k - 1) / 2</math>, not greater than <math>\lceil N / 3 \rceil</math> | |||
| <math>1, 4, 13, 40, 121, \ldots </math> | |||
| <math>\Theta(N^{3/2})</math> | |||
| [[Donald Knuth|Knuth]], 1973<ref name="Knuth">{{Cite book | |||
|last=Knuth | |||
|first=Donald E. | |||
|title=The Art of Computer Programming. Volume 3: Sorting and Searching | |||
|edition=2nd | |||
|publisher=Addison-Wesley | |||
|location=Reading, Massachusetts | |||
|year=1997 | |||
|pages=83–95 | |||
|chapter=Shell's method | |||
|isbn=0-201-89685-0}}</ref> | |||
|---- | |||
| <math>\prod | |||
\limits_{\scriptscriptstyle 0\le q<r\atop | |||
\scriptscriptstyle q\neq(r^2+r)/2-k}a_q, \hbox{where}</math> | |||
:<math>r = \left\lfloor \sqrt{2k+\sqrt{2k}} \right\rfloor,</math> | |||
:<math>a_q=\min\{n\in\mathbb{N}\colon n\ge(5/2)^{q+1},</math> | |||
:<math>\forall p\colon0\le p<q\Rightarrow\gcd(a_p,n)=1\}</math> | |||
| <math>1, 3, 7, 21, 48, 112, \ldots</math> | |||
| <math>O(N e^\sqrt{8\ln(5/2)\ln N})</math> | |||
| Incerpi & [[Robert Sedgewick (computer scientist)|Sedgewick]], 1985<ref>{{Cite journal | |||
|last=Incerpi | |||
|first=Janet | |||
|last2=Sedgewick | |||
|first2=Robert | |||
|title=Improved Upper Bounds on Shellsort | |||
|journal=Journal of Computer and System Sciences | |||
|volume=31 | |||
|issue=2 | |||
|year=1985 | |||
|pages=210–224 | |||
|doi=}}</ref> | |||
|---- | |||
| <math>4^k + 3\cdot2^{k-1} + 1</math>, prefixed with 1 | |||
| <math>1, 8, 23, 77, 281, \ldots</math> | |||
| <math>O(N^{4/3})</math> | |||
| Sedgewick, 1986<ref name="Sedgewick"/> | |||
|---- | |||
| <math>9(4^{k-1}-2^{k-1})+1, 4^{k+1}-6\cdot2^k+1</math> | |||
| <math>1, 5, 19, 41, 109, \ldots</math> | |||
| <math>O(N^{4/3})</math> | |||
| Sedgewick, 1986<ref name="Sedgewick">{{Cite journal | |||
|last=Sedgewick | |||
|first=Robert | |||
|title=A New Upper Bound for Shellsort | |||
|journal=Journal of Algorithms | |||
|volume=7 | |||
|issue=2 | |||
|year=1986 | |||
|pages=159–173 | |||
|doi=10.1016/0196-6774(86)90001-5}}</ref> | |||
|---- | |||
| <math>h_k = \max\left\{\left\lfloor 5h_{k-1}/11 \right\rfloor, 1\right\}, h_0 = N</math> | |||
| <math>\left\lfloor \frac{5N}{11} \right\rfloor, \left\lfloor \frac{5}{11}\left\lfloor \frac{5N}{11} \right\rfloor\right\rfloor, \ldots, 1</math> | |||
| ? | |||
| [[Gaston Gonnet|Gonnet]] & [[Ricardo Baeza-Yates|{{j|Baeza-Yates}}]], 1991<ref name="Gonnet">{{Cite book | |||
|last=Gonnet | |||
|first=Gaston H. | |||
|last2=Baeza-Yates | |||
|first2=Ricardo | |||
|title=Handbook of Algorithms and Data Structures: In Pascal and C | |||
|publisher=Addison-Wesley | |||
|location=Reading, Massachusetts | |||
|edition=2nd | |||
|year=1991 | |||
|pages=161–163 | |||
|chapter=Shellsort | |||
|isbn=0-201-41607-7}}</ref> | |||
|---- | |||
| <math>\left\lceil \frac{9^k-4^k}{5\cdot4^{k-1}} \right\rceil</math> | |||
| <math>1, 4, 9, 20, 46, 103, \ldots</math> | |||
| ? | |||
| Tokuda, 1992<ref>{{Cite book | |||
|editor-last=van Leeuven | |||
|editor-first=Jan | |||
|chapter=An Improved Shellsort | |||
|last=Tokuda | |||
|first=Naoyuki | |||
|title=Proceedings of the IFIP 12th World Computer Congress on Algorithms, Software, Architecture | |||
|publisher=North-Holland Publishing Co. | |||
|location=Amsterdam | |||
|year=1992 | |||
|pages=449–457 | |||
|isbn=0-444-89747-X}}</ref> | |||
|---- | |||
| unknown | |||
| <math>1, 4, 10, 23, 57, 132, 301, 701</math> | |||
| ? | |||
| Ciura, 2001<ref>{{Cite book | |||
|url=http://sun.aei.polsl.pl/~mciura/publikacje/shellsort.pdf | |||
|title=Proceedings of the 13th International Symposium on Fundamentals of Computation Theory | |||
|editor-last=Freiwalds | |||
|editor-first=Rusins | |||
|last=Ciura | |||
|first=Marcin | |||
|chapter=Best Increments for the Average Case of Shellsort | |||
|publisher=Springer-Verlag | |||
|location=London | |||
|year=2001 | |||
|pages=106–117 | |||
|isbn=3-540-42487-3}}</ref> | |||
|} | |||
When the binary representation of ''N'' contains many consecutive zeroes, Shellsort using Shell's original gap sequence makes Θ(''N''<sup>2</sup>) comparisons in the worst case. For instance, this case occurs for ''N'' equal to a power of two when elements greater and smaller than the median occupy odd and even positions respectively, since they are compared only in the last pass. | |||
Although it has higher complexity than the ''O''(''N''log''N'') that is optimal for comparison sorts, Pratt's version lends itself to [[sorting network]]s and has the same asymptotic gate complexity as Batcher's [[bitonic sorter]]. | |||
Gonnet and Baeza-Yates observed that Shellsort makes the fewest comparisons on average when the ratios of successive gaps are roughly equal to 2.2.<ref name="Gonnet"/> This is why their sequence with ratio 2.2 and Tokuda's sequence with ratio 2.25 prove efficient. However, it is not known why this is so. Sedgewick recommends to use gaps that have low [[greatest common divisor]]s or are pairwise [[coprime]].<ref>{{Cite book | |||
|title=Algorithms in C++, Parts 1-4: Fundamentals, Data Structure, Sorting, Searching | |||
|last=Sedgewick | |||
|first=Robert | |||
|chapter=Shellsort | |||
|publisher=Addison-Wesley | |||
|location=Reading, Massachusetts | |||
|year=1998 | |||
|pages=285–292 | |||
|isbn=0-201-35088-2}}</ref> | |||
With respect to the average number of comparisons, the best known gap sequences are 1, 4, 10, 23, 57, 132, 301, 701 and similar, with gaps found experimentally. Optimal gaps beyond 701 remain unknown, but good results can be obtained by extending the above sequence according to the recursive formula <math>h_k = \lfloor 2.25 h_{k-1} \rfloor</math>. | |||
Tokuda's sequence, defined by the simple formula <math>h_k = \lceil h'_k \rceil</math>, where <math>h'_k = 2.25 h'_{k-1} + 1</math>, <math>h'_1 = 1</math>, can be recommended for practical applications. | |||
== Computational complexity == | |||
The following property holds: after ''h''<sub>2</sub>-sorting of any ''h''<sub>1</sub>-sorted array, the array remains ''h''<sub>1</sub>-sorted.<ref>{{Cite journal | |||
|last=Gale | |||
|first=David | |||
|last2=Karp | |||
|first2=Richard M. | |||
|title=A Phenomenon in the Theory of Sorting | |||
|journal=Journal of Computer and System Sciences | |||
|volume=6 | |||
|issue=2 | |||
|year=1972 | |||
|pages=103–115 | |||
|doi=10.1016/S0022-0000(72)80016-3}}</ref> Every ''h''<sub>1</sub>-sorted and ''h''<sub>2</sub>-sorted array is also (''a''<sub>1</sub>''h''<sub>1</sub>+''a''<sub>2</sub>''h''<sub>2</sub>)-sorted, for any nonnegative integers ''a''<sub>1</sub> and ''a''<sub>2</sub>. The worst-case complexity of Shellsort is therefore connected with the [[coin problem|Frobenius problem]]: for given integers ''h''<sub>1</sub>,..., ''h''<sub>''n''</sub> with gcd = 1, the Frobenius number ''g''(''h''<sub>1</sub>,..., ''h''<sub>''n''</sub>) is the greatest integer that cannot be represented as ''a''<sub>1</sub>''h''<sub>1</sub>+ ... +''a''<sub>''n''</sub>''h''<sub>''n''</sub> with nonnegative integer ''a''<sub>1</sub>,..., ''a''<sub>''n''</sub>. Using known formulae for Frobenius numbers, we can determine the worst-case complexity of Shellsort for several classes of gap sequences.<ref>{{Cite journal | |||
|last=Selmer | |||
|first=Ernst S. | |||
|title=On Shellsort and the Frobenius Problem | |||
|journal=BIT Numerical Mathematics | |||
|volume=29 | |||
|issue=1 | |||
|year=1989 | |||
|pages=37–40 | |||
|doi=10.1007/BF01932703}}</ref> Proven results are shown in the above table. | |||
With respect to the average number of operations, none of proven results concerns a practical gap sequence. For gaps that are powers of two, Espelid computed this average as <math>0.5349N\sqrt{N}-0.4387N-0.097\sqrt{N}+O(1)</math>.<ref>{{Cite journal | |||
|last=Espelid | |||
|first=Terje O. | |||
|title=Analysis of a Shellsort Algorithm | |||
|journal=BIT Numerical Mathematics | |||
|volume=13 | |||
|issue=4 | |||
|year=1973 | |||
|pages=394–400 | |||
|doi=10.1007/BF01933401}}</ref> [[Donald Knuth|Knuth]] determined the average complexity of sorting an ''N''-element array with two gaps (''h'', 1) to be <math>2N^2/h + \sqrt{\pi N^3 h}</math>.<ref name="Knuth" /> It follows that a two-pass Shellsort with ''h'' = Θ(''N''<sup>1/3</sup>) makes on average ''O''(''N''<sup>5/3</sup>) comparisons. [[Andrew Yao|Yao]] found the average complexity of a three-pass Shellsort.<ref>{{Cite journal | |||
|last=Yao | |||
|first=Andrew Chi-Chih | |||
|title=An Analysis of (''h'', ''k'', 1)-Shellsort | |||
|journal=Journal of Algorithms | |||
|volume=1 | |||
|issue=1 | |||
|year=1980 | |||
|pages=14–50 | |||
|doi=10.1016/0196-6774(80)90003-6}}</ref> His result was refined by Janson and Knuth:<ref>{{Cite journal | |||
|arxiv=cs/9608105 | |||
|id=[[CiteSeerX]]: {{url|1=citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.54.9911|2=10.1.1.54.9911}} | |||
|last=Janson | |||
|first=Svante | |||
|last2=Knuth | |||
|first2=Donald E. | |||
|title=Shellsort with Three Increments | |||
|journal=Random Structures and Algorithms | |||
|volume=10 | |||
|issue=1-2 | |||
|year=1997 | |||
|pages=125–142 | |||
|doi=10.1002/(SICI)1098-2418(199701/03)10:1/2<125::AID-RSA6>3.0.CO;2-X}}</ref> the average number of comparisons made during a Shellsort with three gaps (''ch'', ''cg'', 1), where ''h'' and ''g'' are coprime, is <math>\frac{N^2}{4ch}+O(N)</math> in the first pass, <math>\frac{1}{8g}\sqrt{\frac{\pi}{ch}}(h-1)N^{3/2}+O(hN)</math> in the second pass and <math>\psi(h, g)N + \frac{1}{8}\sqrt{\frac{\pi}{c}}(c-1)N^{3/2}+O((c-1)gh^{1/2}N) + O(c^2g^3h^2)</math> in the third pass. ''ψ''(''h'', ''g'') in the last formula is a complicated function asymptotically equal to <math>\sqrt{\frac{\pi h}{128}}g + O(g^{-1/2}h^{1/2}) + O(gh^{-1/2})</math>. In particular, when ''h'' = Θ(''N''<sup>7/15</sup>) and ''g'' = Θ(''h''<sup>1/5</sup>), the average time of sorting is ''O''(''N''<sup>23/15</sup>). | |||
Based on experiments, it is conjectured that Shellsort with Hibbard's and Knuth's gap sequences runs in ''O''(''N''<sup>5/4</sup>) average time,<ref name="Knuth" /> and that Gonnet and Baeza-Yates's sequence requires on average 0.41''N''ln''N''(ln ln''N''+1/6) element moves.<ref name="Gonnet" /> Approximations of the average number of operations formerly put forward for other sequences fail when sorted arrays contain millions of elements. | |||
The graph below shows the average number of element comparisons in various variants of Shellsort, divided by the theoretical lower bound, i.e. log<sub>2</sub>''N''!, where the sequence 1, 4, 10, 23, 57, 132, 301, 701 has been extended according to the formula <math>h_k = \lfloor2.25 h_{k-1}\rfloor</math>. | |||
[[File:Shell sort average number of comparisons (English).svg|center]] | |||
Applying the theory of [[Kolmogorov complexity]], Jiang, Li, and [[Paul Vitanyi|Vitányi]] proved the following lower bounds for the order of the average number of operations in an ''m''-pass Shellsort: Ω(''mN''<sup>1+1/''m''</sup>) when ''m''≤log<sub>2</sub>''N'' and Ω(''mN'') when ''m''>log<sub>2</sub>''N''.<ref>{{Cite journal | |||
|id = [[CiteSeerX]]: {{url|1=citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.6.6508|2=10.1.1.6.6508}} | |||
|last=Jiang | |||
|first=Tao | |||
|last2=Li | |||
|first2=Ming | |||
|last3=Vitányi | |||
|first3=Paul | |||
|title=A Lower Bound on the Average-Case Complexity of Shellsort | |||
|journal=[[Journal of the ACM]] | |||
|volume=47 | |||
|issue=5 | |||
|year=2000 | |||
|pages=905–911 | |||
|doi=10.1145/355483.355488}}</ref> Therefore Shellsort has prospects of running in an average time that asymptotically grows like ''N''log''N'' only when using gap sequences whose number of gaps grows in proportion to the logarithm of the array size. It is, however, unknown whether Shellsort can reach this asymptotic order of average-case complexity, which is optimal for comparison sorts. | |||
The worst-case complexity of any version of Shellsort is of higher order: Plaxton, Poonen, and [[Torsten Suel|Suel]] showed that it grows at least as rapidly as Ω(''N''(log''N''/log log''N'')<sup>2</sup>).<ref>{{Cite journal | |||
|id=[[CiteSeerX]]: {{url|1=citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.43.1393|2=10.1.1.43.1393}} | |||
|last=Plaxton | |||
|first=C. Greg | |||
|last2=Poonen | |||
|first2=Bjarne | |||
|last3=Suel | |||
|first3=Torsten | |||
|title=Improved Lower Bounds for Shellsort | |||
|journal=Annual Symposium on Foundations of Computer Science | |||
|volume=33 | |||
|year=1992 | |||
|pages=226–235 | |||
|doi=10.1109/SFCS.1992.267769 | |||
}}</ref> | |||
== Applications == | |||
Shellsort is now rarely used in serious applications. It performs more operations and has higher [[CPU cache#Cache_miss|cache miss ratio]] than [[quicksort]]. However, since it can be implemented using little code and does not use the [[call stack]], some implementations of the [[qsort]] function in the [[C standard library]] targeted at [[embedded systems]] use it instead of quicksort. Shellsort is, for example, used in the [[uClibc]] library.<ref>{{Cite web | |||
| url=http://git.uclibc.org/uClibc/tree/libc/stdlib/stdlib.c#n786 | |||
| title=libc/stdlib/stdlib.c | |||
| author=Manuel Novoa III | |||
| accessdate=2011-03-30}}</ref> For similar reasons, an implementation of Shellsort is present in the [[Linux kernel]].<ref>{{Cite web | |||
| url=https://github.com/torvalds/linux/blob/72932611b4b05bbd89fafa369d564ac8e449809b/kernel/groups.c#L105 | |||
| title=kernel/groups.c | |||
| accessdate=2012-05-05}}</ref> | |||
Shellsort can also serve as a sub-algorithm of [[introsort|introspective sort]], to sort short subarrays and to prevent a pathological slowdown when the recursion depth exceeds a given limit. This principle is employed, for instance, in the [[bzip2]] compressor.<ref>{{Cite web | |||
|url=http://www.ncbi.nlm.nih.gov/IEB/ToolBox/CPP_DOC/lxr/source/src/util/compress/bzip2/blocksort.c#L519 | |||
|title=bzip2/blocksort.c | |||
|author=Julian Seward | |||
|accessdate=2011-03-30}}</ref> | |||
== See also == | |||
* [[Comb sort]] | |||
== References == | |||
{{reflist|30em}} | |||
== Bibliography == | |||
* {{Cite book | |||
|last=Knuth | |||
|first=Donald E. | |||
|title=The Art of Computer Programming. Volume 3: Sorting and Searching | |||
|edition=2nd | |||
|publisher=Addison-Wesley | |||
|location=Reading, Massachusetts | |||
|year=1997 | |||
|pages=83–95 | |||
|chapter=Shell's method | |||
|isbn=0-201-89685-0 | |||
}} | |||
* [http://www.cs.princeton.edu/~rs/shell/ Analysis of Shellsort and Related Algorithms], Robert Sedgewick, Fourth European Symposium on Algorithms, Barcelona, September 1996. | |||
== External links == | |||
{{wikibooks|Algorithm implementation|Sorting/Shell_sort|Shell sort}} | |||
* [http://www.youtube.com/watch?v=CmPA7zE8mx0 Shellsort with gaps 5, 3, 1 as a Hungarian folk dance] | |||
{{sorting}} | |||
{{Use dmy dates|date=September 2010}} | |||
{{DEFAULTSORT:Shellsort}} | |||
[[Category:Sorting algorithms]] | |||
[[Category:Comparison sorts]] | |||
{{link GA|pl}} |
Revision as of 20:15, 14 January 2014
Template:Infobox Algorithm Shellsort, also known as Shell sort or Shell's method, is an in-place comparison sort. It generalizes an exchanging sort, such as insertion or bubble sort, by starting the comparison and exchange of elements with elements that are far apart before finishing with neighboring elements. Starting with far apart elements can move some out-of-place elements into position faster than a simple nearest neighbor exchange. Donald Shell published the first version of this sort in 1959.[1][2] The running time of Shellsort is heavily dependent on the gap sequence it uses. For many practical variants, determining their time complexity remains an open problem.
Description
Shellsort is a generalization of insertion sort that allows the exchange of items that are far apart. The idea is to arrange the list of elements so that, starting anywhere, considering every hth element gives a sorted list. Such a list is said to be h-sorted. Equivalently, it can be thought of as h interleaved lists, each individually sorted.[3] Beginning with large values of h, this rearrangement allows elements to move long distances in the original list, reducing large amounts of disorder quickly, and leaving less work for smaller h-sort steps to do.[4] If the file is then k-sorted for some smaller integer k, then the file remains h-sorted. Following this idea for a decreasing sequence of h values ending in 1 is guaranteed to leave a sorted list in the end.[3]
An example run of Shellsort with gaps 5, 3 and 1 is shown below.
The first pass, 5-sorting, performs insertion sort on separate subarrays (a1, a6, a11), (a2, a7, a12), (a3, a8), (a4, a9), (a5, a10). For instance, it changes the subarray (a1, a6, a11) from (62, 17, 25) to (17, 25, 62). The next pass, 3-sorting, performs insertion sort on the subarrays (a1, a4, a7, a10), (a2, a5, a8, a11), (a3, a6, a9, a12). The last pass, 1-sorting, is an ordinary insertion sort of the entire array (a1,..., a12).
As the example illustrates, the subarrays that Shellsort operates on are initially short; later they are longer but almost ordered. In both cases insertion sort works efficiently.
Shellsort is unstable: it may change the relative order of elements with equal values. It has "natural" behavior, in that it executes faster when the input is partially sorted.
Pseudocode
Using Marcin Ciura's gap sequence, with an inner insertion sort.
# Sort an array a[0...n-1]. gaps = [701, 301, 132, 57, 23, 10, 4, 1] foreach (gap in gaps) { # Do an insertion sort for each gap size. for (i = gap; i < n; i += 1) { temp = a[i] for (j = i; j >= gap and a[j - gap] > temp; j -= gap) { a[j] = a[j - gap] } a[j] = temp } }
Gap sequences
The question of deciding which gap sequence to use is difficult. Every gap sequence that contains 1 yields a correct sort; however, the properties of thus obtained versions of Shellsort may be very different.
The table below compares most proposed gap sequences published so far. Some of them have decreasing elements that depend on the size of the sorted array (N). Others are increasing infinite sequences, whose elements less than N should be used in reverse order.
General term (k ≥ 1) Concrete gaps Worst-case
time complexityAuthor and year of publication [when N=2p] Shell, 1959[1] Frank & Lazarus, 1960[5] Hibbard, 1963[6] , prefixed with 1 Papernov & Stasevich, 1965[7] successive numbers of the form Pratt, 1971[8] , not greater than Knuth, 1973[9] Incerpi & Sedgewick, 1985[10] , prefixed with 1 Sedgewick, 1986[3] Sedgewick, 1986[3] ? Gonnet & [[Ricardo Baeza-Yates|Template:J]], 1991[11] ? Tokuda, 1992[12] unknown ? Ciura, 2001[13]
When the binary representation of N contains many consecutive zeroes, Shellsort using Shell's original gap sequence makes Θ(N2) comparisons in the worst case. For instance, this case occurs for N equal to a power of two when elements greater and smaller than the median occupy odd and even positions respectively, since they are compared only in the last pass.
Although it has higher complexity than the O(NlogN) that is optimal for comparison sorts, Pratt's version lends itself to sorting networks and has the same asymptotic gate complexity as Batcher's bitonic sorter.
Gonnet and Baeza-Yates observed that Shellsort makes the fewest comparisons on average when the ratios of successive gaps are roughly equal to 2.2.[11] This is why their sequence with ratio 2.2 and Tokuda's sequence with ratio 2.25 prove efficient. However, it is not known why this is so. Sedgewick recommends to use gaps that have low greatest common divisors or are pairwise coprime.[14]
With respect to the average number of comparisons, the best known gap sequences are 1, 4, 10, 23, 57, 132, 301, 701 and similar, with gaps found experimentally. Optimal gaps beyond 701 remain unknown, but good results can be obtained by extending the above sequence according to the recursive formula .
Tokuda's sequence, defined by the simple formula , where , , can be recommended for practical applications.
Computational complexity
The following property holds: after h2-sorting of any h1-sorted array, the array remains h1-sorted.[15] Every h1-sorted and h2-sorted array is also (a1h1+a2h2)-sorted, for any nonnegative integers a1 and a2. The worst-case complexity of Shellsort is therefore connected with the Frobenius problem: for given integers h1,..., hn with gcd = 1, the Frobenius number g(h1,..., hn) is the greatest integer that cannot be represented as a1h1+ ... +anhn with nonnegative integer a1,..., an. Using known formulae for Frobenius numbers, we can determine the worst-case complexity of Shellsort for several classes of gap sequences.[16] Proven results are shown in the above table.
With respect to the average number of operations, none of proven results concerns a practical gap sequence. For gaps that are powers of two, Espelid computed this average as .[17] Knuth determined the average complexity of sorting an N-element array with two gaps (h, 1) to be .[9] It follows that a two-pass Shellsort with h = Θ(N1/3) makes on average O(N5/3) comparisons. Yao found the average complexity of a three-pass Shellsort.[18] His result was refined by Janson and Knuth:[19] the average number of comparisons made during a Shellsort with three gaps (ch, cg, 1), where h and g are coprime, is in the first pass, in the second pass and in the third pass. ψ(h, g) in the last formula is a complicated function asymptotically equal to . In particular, when h = Θ(N7/15) and g = Θ(h1/5), the average time of sorting is O(N23/15).
Based on experiments, it is conjectured that Shellsort with Hibbard's and Knuth's gap sequences runs in O(N5/4) average time,[9] and that Gonnet and Baeza-Yates's sequence requires on average 0.41NlnN(ln lnN+1/6) element moves.[11] Approximations of the average number of operations formerly put forward for other sequences fail when sorted arrays contain millions of elements.
The graph below shows the average number of element comparisons in various variants of Shellsort, divided by the theoretical lower bound, i.e. log2N!, where the sequence 1, 4, 10, 23, 57, 132, 301, 701 has been extended according to the formula .
![](https://upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Shell_sort_average_number_of_comparisons_%28English%29.svg/512px-Shell_sort_average_number_of_comparisons_%28English%29.svg.png)
Applying the theory of Kolmogorov complexity, Jiang, Li, and Vitányi proved the following lower bounds for the order of the average number of operations in an m-pass Shellsort: Ω(mN1+1/m) when m≤log2N and Ω(mN) when m>log2N.[20] Therefore Shellsort has prospects of running in an average time that asymptotically grows like NlogN only when using gap sequences whose number of gaps grows in proportion to the logarithm of the array size. It is, however, unknown whether Shellsort can reach this asymptotic order of average-case complexity, which is optimal for comparison sorts.
The worst-case complexity of any version of Shellsort is of higher order: Plaxton, Poonen, and Suel showed that it grows at least as rapidly as Ω(N(logN/log logN)2).[21]
Applications
Shellsort is now rarely used in serious applications. It performs more operations and has higher cache miss ratio than quicksort. However, since it can be implemented using little code and does not use the call stack, some implementations of the qsort function in the C standard library targeted at embedded systems use it instead of quicksort. Shellsort is, for example, used in the uClibc library.[22] For similar reasons, an implementation of Shellsort is present in the Linux kernel.[23]
Shellsort can also serve as a sub-algorithm of introspective sort, to sort short subarrays and to prevent a pathological slowdown when the recursion depth exceeds a given limit. This principle is employed, for instance, in the bzip2 compressor.[24]
See also
References
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Bibliography
- 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - Analysis of Shellsort and Related Algorithms, Robert Sedgewick, Fourth European Symposium on Algorithms, Barcelona, September 1996.
External links
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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
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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 - ↑ Some older textbooks and references call this the "Shell-Metzner" sort after Marlene Metzner Norton, but according to Metzner, "I had nothing to do with the sort, and my name should never have been attached to it." See Template:Cite web
- ↑ 3.0 3.1 3.2 3.3 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 Cite error: Invalid<ref>
tag; name "Sedgewick" defined multiple times with different content - ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ 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 - ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ 9.0 9.1 9.2 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ 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 - ↑ 11.0 11.1 11.2 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ 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 - ↑ Template:Cite web
- ↑ Template:Cite web
- ↑ Template:Cite web