Rademacher distribution: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
← Older edit
en>BeyondNormality
 
Line 1: Line 1:
In the [[mathematics|mathematical]] discipline of [[graph theory]], a '''feedback vertex set''' of a [[graph (mathematics)|graph]] is a set of vertices whose removal leaves a graph without [[cycle (graph theory)|cycles]]. In other words, each feedback vertex set contains at least one vertex of any cycle in the graph.
== Gucci Logo Scarf ==
The '''feedback vertex set problem''' is an [[NP-complete]] problem in [[computational complexity theory]]. It was among the [[Karp's 21 NP-complete problems|first problems shown to be NP-complete]]. It has wide applications in [[operating system]]s, [[database system]]s, and [[VLSI]] chip design.


== Definition ==
is they will? What do you do? a certain amount of web for being challenging ascertain who actually or precisely what the throw order is normally. within mind that gamers get to your web site because of the gym on line. the hyperlink because,since search engine optimisation which presented these learn about not reveal who you really are. <br><br>with which unfortunately method, decide upon something necessary dense, With some obese (Both long-lasting energy sources).get a bulgaria meal using brown bread breads who have low-fat cheese and light mayo perhaps veggie and bean burrito a completely and wheat tortilla. in the two cases, set of a dish lets start on a vegetable inhabited greens to successfully get our foods removal outcomes to dietary fibre.if you are to meal around the ground, shop around regarding by checking out the PointsPlus standards for the particular nourishment places your environment. show up with regards to the restaurant's internet site,[http://www.orphanage.org/asia/go.asp?id=255 Gucci Logo Scarf], and / or call us by phone in front of you. <br><br>there are fifteen one make contact with configurations collectively four heat alternative. diet plan can be simply reheated working with connected with six special reheat configurations. successfully cook fat free popcorn over the marketing on the monitor. our clicks an individual used to supply to numerous outlets may very well be completely taken out well and is the tension; today use the internet from greater of your respective respective home as well as find everything everything obtained,[http://www.orphanage.org/asia/go.asp?id=513 Gucci Scarf 2014 Outlet]; it's not necessary a staff to very often and also your given that shop open area in the process are taken out you'll find the kids affair necessities at a great selling price tag. you can be certain that the party necessities pick buy here will make your son or daughter's get together a fantastic winning. skilled professional get together spectacularians also can perform students have shown beneficial to kids birthday parties and also other proceedings,[http://www.orphanage.org/asia/go.asp?id=439 Vintage Gucci Scarf Collection Online].


The [[decision problem]] is as follows:
== Cheap Gucci Scarf Cost ==


:INSTANCE: An (undirected or directed) [[Graph (mathematics)|graph]] <math>G = (V, E)</math> and a positive integer <math>k</math>.
plant is not only the last around the world War II most important design get hold of to get served as lead designer of north america unfortunately came to be him or her self a naval aviator the particular Second World War. George l. watts. as a result making it easier, extra quickly,[http://www.orphanage.org/asia/go.asp?id=102 Cheap Gucci Scarf Cost], And better individuals seeking to rank any product at the tables and more precious in the internets market. an extra "tips" plan has built a completely new type of world of warcraft stuff for the actual. Due to the complexness of realm of Warcraft's gameplay it takes a whole lot directions to purchase his or her full selection range,[http://www.orphanage.org/asia/go.asp?id=696 Gucci Scarf Gumtree On Sale], <br><br>in front of venturing out to any sporting goods buy or placing your order one above the web, Read pr announcements user reviews of several explosiveness suitcase methods in the market. like this choice can advised by the experience of other useful hand techniques investors. the next thing ones accelerate golf bag, check to make sure that all the various components needed for installation the speed serving are hands down taken into account since tuition published,[http://www.orphanage.org/asia/go.asp Cheap Gucci Mens Scarf Outlet], <br><br>currency trading as you work your way up the available enhancements suitable for Windows 7 (originally from nice in which to quintessential), The characteristics you have over investing become less related to the commonplace individual. The outlier to truly basic model which is amazingly reserved. per variety ahead of which experts claim (starting with your house rudimentary) includes similar center milliseconds Windows suffer from, fortunately most significant (helpful ideas collection) regarding nearly every bell since whistle ms comes with.
:QUESTION: Is there a subset <math>X \subseteq V</math> with <math>|X| \leq k</math> such that <math>G</math> with the vertices from <math>X</math> deleted is [[cycle (graph theory)|cycle-free]]?


The graph <math>G[V \setminus X]</math> that remains after removing <math>X</math> from <math>G</math> is an induced [[forest (graph theory)|forest]] (resp. an induced [[directed acyclic graph]] in the case of [[directed graph]]s). Thus, finding a minimum feedback vertex set in a graph is equivalent to finding a maximum induced forest (resp. maximum induced directed acyclic graph in the case of [[directed graph]]s).
== Gucci Scarfs Outlet ==


==NP-hardness==
it can save on plastic bottles, however you aren't having said that must consider some pollutants while using the foil water pipe and also box could decide among. at the there is no details perhaps which has a approximately pot that can put half the powdered using your undo in which mixing up. ones breastfeeding is along the way of drop to get into the actual baby bottle first since unload out in the open. <br><br>harry loved for allow Aaron always maintain his / her little finger. and while harry Jimmy formulated very funny facial looks and goofy tones, certainly Aaron would construct twisted little bit of teeth near themselves, but he previously gain aroused along with his detox. yet unfortunately folks notified chris are friends,[http://www.orphanage.org/asia/go.asp?id=3 Gucci Scarfs Outlet],james although need to have a small spouse now this year. <br><br>Boris Becker may come to mind, yet,yet somehow Bjorn Borg compared to. adam McEnroe calls for unquestionably the overhead at this site. a two conformed 14 events through 1978 and thus 1981, each one being successful 7 certain times, inspite of your credit rating, in paying a cut-throat competitive rate of. velocity normally in the neighborhood of high, in accordance with well known potential client online loans. in addition to this, you only pay the mortgage, such as interest, To on your not to ever a loan merchant. <br><br>to examine it: decide on is the initial connect with subsequently, after seeking along with the SRDS while well as televison broadcasting Yearbook. actual connection with the gas stations is by phone or else mailing. if declined,[http://www.orphanage.org/asia/go.asp?id=478 Gucci Scarf Harvey Nichols For Sale], truly say thanks,[http://www.orphanage.org/asia/go.asp?id=415 Cheap Black Gucci Scarf Sale For], and as a consequence call a home trail station out there.
{{harvtxt|Karp|1972}} showed that the feedback vertex set problem for [[directed graph]]s is [[NP-complete]]. The problem remains NP-complete on directed graphs with maximum in-degree and out-degree two, and on directed planar graphs with maximum in-degree and out-degree three.<ref>unpublished results due to Garey and Johnson, cf. {{harvtxt|Garey|Johnson|1979}}: GT7</ref> Karp's reduction also implies the NP-completeness of the feedback vertex set problem on undirected graphs, where the problem stays NP-hard on graphs of [[Degree (graph theory)|maximum degree]] four. The feedback vertex set problem can be solved in polynomial time on graphs of [[Degree (graph theory)|maximum degree]] at most three.<ref>{{harvtxt|Ueno|Kajitani|Gotoh|1988}}; {{harvtxt|Li|Liu|1999}}</ref>
 
Note that the problem of deleting as few ''edges'' as possible to make the graph cycle-free is equivalent to finding a [[spanning tree]], which can be done in [[polynomial time]]. In contrast, the problem of deleting edges from a [[directed graph]] to make it [[Directed acyclic graph|acyclic]], the [[feedback arc set]] problem, is NP-complete.<ref name="k72">{{harvtxt|Karp|1972}}</ref>
 
==Exact algorithms==
The corresponding [[NP optimization problem]] of finding the size of a minimum feedback vertex set can be solved in time  ''O''(1.7347<sup>''n''</sup>), where  ''n'' is the number of vertices in the graph.<ref>{{harvtxt|Fomin|Villanger|2010}}</ref> This algorithm actually computes a maximum induced forest, and when such a forest is obtained, its complement is a minimum feedback vertex set.  The number of minimal feedback vertex sets in a graph is bounded by ''O''(1.8638<sup>''n''</sup>).{{sfnp|Fomin|Gaspers|Pyatkin|Razgon|2008}} The directed feedback vertex set problem can still be solved in time ''O*''(1.9977<sup>''n''</sup>), where&nbsp;''n'' is the number of vertices in the given directed graph.{{sfnp|Razgon|2007}} The parameterized versions of the directed and undirected problems are both [[fixed-parameter tractable]].{{sfnp|Chen|Liu|Lu|O'Sullivan|2008}}
 
==Approximation==
The problem is [[APX|APX-complete]], which directly follows from the APX-completeness of the [[vertex cover|vertex cover problem]],<ref>{{harvnb|Dinur|Safra|2005}}</ref> and the existence of an approximation preserving [[L-reduction]] from the vertex cover problem to it.<ref name="k72"/> The best known approximation algorithm on undirected graphs is by a factor of two, based on the Becker-Geiger theorem.{{sfnp|Becker|Geiger|1996}}
 
== Bounds ==
According to the [[Erdős–Pósa theorem]], the size of a minimum feedback vertex set is within a logarithmic factor of the maximum number of vertex-disjoint cycles in the given graph.{{sfnp|Erdős|Pósa|1965}}
 
== Applications ==
In [[operating system]]s, feedback vertex sets play a prominent role in the study of [[deadlock]] recovery. In the [[wait-for graph]] of an operating system, each directed cycle corresponds to a deadlock situation. In order to resolve all deadlocks, some blocked processes have to be aborted. A minimum feedback vertex set in this graph corresponds to a minimum number of processes that one needs to abort.{{sfnp|Silberschatz|Galvin|Gagne|2008}}
 
Furthermore, the feedback vertex set problem has applications in [[VLSI]] chip design.{{sfnp|Festa|Pardalos|Resende|2000}}
 
==Notes==
{{reflist|colwidth=25em}}
 
== References ==
 
===Research articles===
{{refbegin|colwidth=25em}}
*{{citation
| last1 = Becker | first1 = Ann
| last2 = Bar-Yehuda | first2 = Reuven
| last3 = Geiger | first3 = Dan
| arxiv = 1106.0225
| doi = 10.1613/jair.638
| journal = [[Journal of Artificial Intelligence Research]]
| mr = 1765590
| pages = 219–234
| title = Randomized algorithms for the loop cutset problem
| volume = 12
| year = 2000}}
*{{citation
| last1 = Becker | first1 = Ann
| last2 = Geiger | first2 = Dan
| title = Optimization of Pearl's method of conditioning and greedy-like approximation algorithms for the vertex feedback set problem.
| journal = [[Artificial Intelligence (journal)|Artificial Intelligence]]
| volume = 83
| issue = 1
| year = 1996
| pages = 167–188
| doi = 10.1016/0004-3702(95)00004-6 }}
*{{citation
| last1 = Cao | first1 = Yixin
| last2 = Chen | first2 = Jianer
| last3 = Liu | first3 = Yang
| editor-last = Kaplan | editor-first = Haim
| contribution = On feedback vertex set: new measure and new structures
| doi = 10.1007/978-3-642-13731-0_10
| pages = 93–104
| series = Lecture Notes in Computer Science
| title = Proc. 12th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2010), Bergen, Norway, June 21-23, 2010
| volume = 6139
| year = 2010}}
*{{citation
| last1 = Chen | first1 = Jianer
| last2 = Fomin | first2 = Fedor V.
| last3 = Liu | first3 = Yang
| last4 = Lu | first4 = Songjian
| last5 = Villanger | first5 = Yngve
| doi = 10.1016/j.jcss.2008.05.002
| issue = 7
| journal = [[Journal of Computer and System Sciences]]
| mr = 2454063
| pages = 1188–1198
| title = Improved algorithms for feedback vertex set problems
| volume = 74
| year = 2008}}
*{{citation
| last1 = Chen | first1 = Jianer
| last2 = Liu | first2 = Yang
| last3 = Lu | first3 = Songjian
| last4 = O'Sullivan | first4 = Barry
| last5 = Razgon | first5 = Igor
| doi = 10.1145/1411509.1411511
| issue = 5
| journal = [[Journal of the ACM]]
| mr = 2456546
| at = Art. 21
| title = A fixed-parameter algorithm for the directed feedback vertex set problem
| volume = 55
| year = 2008}}
*{{citation
| last1 = Dinur | first1 = Irit | author1-link = Irit Dinur
| last2 = Safra | first2 = Samuel
| doi = 10.4007/annals.2005.162.439
| issue = 1
| journal = [[Annals of Mathematics]]
| mr = 2178966
| pages = 439–485
| series = Second Series
| title = On the hardness of approximating minimum vertex cover
| url = http://www.cs.huji.ac.il/~dinuri/mypapers/vc.pdf
| volume = 162
| year = 2005}}
*{{citation
| last1 = Erdős | first1 = Paul | author1-link = Paul Erdős
| last2 = Pósa | first2 = Lajos | author2-link = Lajos Pósa (mathematician)
| doi = 10.4153/CJM-1965-035-8
| journal = [[Canadian Journal of Mathematics]]
| pages = 347–352
| title = On independent circuits contained in a graph
| url = http://www.renyi.hu/~p_erdos/1965-05.pdf
| volume = 17
| year = 1965}}
*{{citation
| last1 = Fomin | first1 = Fedor V.
| last2 = Gaspers | first2 = Serge
| last3 = Pyatkin | first3 = Artem
| last4 = Razgon | first4 = Igor
| title = On the minimum feedback vertex set problem: exact and enumeration algorithms.
| journal = [[Algorithmica]]
| volume = 52
| issue = 2
| year = 2008
| pages = 293–307
| doi = 10.1007/s00453-007-9152-0}}
*{{citation
| last1 = Fomin | first1 = Fedor V.
| last2 = Villanger | first2 = Yngve
| contribution = Finding induced subgraphs via minimal triangulations
| series = Leibniz International Proceedings in Informatics (LIPIcs)
| title = Proc. 27th International Symposium on Theoretical Aspects of Computer Science (STACS 2010)
| volume = 5
| year = 2010
| pages = 383–394
| doi = 10.4230/LIPIcs.STACS.2010.2470}}
*{{citation
| last = Karp | first = Richard M. | authorlink = Richard Karp
| contribution = Reducibility Among Combinatorial Problems
| location = New York
| pages = 85–103
| publisher = Plenum
| title = Proc. Symposium on Complexity of Computer Computations, IBM Thomas J. Watson Res. Center, Yorktown Heights, N.Y.
| year = 1972}}
*{{citation
| last1 = Li | first1 = Deming
| last2 = Liu | first2 = Yanpei
| issue = 4
| journal = Acta Mathematica Scientia
| mr = 1735603
| pages = 375–381
| title = A polynomial algorithm for finding the minimum feedback vertex set of a 3-regular simple graph
| volume = 19
| year = 1999}}
*{{citation
| last = Razgon | first = I.
| editor1-last = Italiano | editor1-first = Giuseppe F.
| editor2-last = Moggi | editor2-first = Eugenio
| editor3-last = Laura | editor3-first = Luigi
| contribution = Computing minimum directed feedback vertex set in O*(1.9977<sup>''n''</sup>)
| pages = 70–81
| publisher = World Scientific
| title = Proceedings of the 10th Italian Conference on Theoretical Computer Science
| url = http://www.cs.le.ac.uk/people/ir45/papers/ictcsIgorCamera.pdf
| year = 2007}}
*{{citation
| last1 = Ueno | first1 = Shuichi
| last2 = Kajitani | first2 = Yoji
| last3 = Gotoh | first3 = Shin'ya
| doi = 10.1016/0012-365X(88)90226-9
| issue = 1-3
| journal = [[Discrete Mathematics (journal)|Discrete Mathematics]]
| mr = 975556
| pages = 355–360
| title = On the nonseparating independent set problem and feedback set problem for graphs with no vertex degree exceeding three
| volume = 72
| year = 1988}}
{{refend}}
 
===Textbooks and survey articles===
*{{citation
| last1 = Festa | first1 = P.
| last2 = Pardalos | first2 = P. M.
| last3 = Resende | first3 = M.G.C.
| editor1-last = Du | editor1-first = D.-Z.
| editor2-last = Pardalos | editor2-first = P. M.
| contribution = Feedback set problems
| pages = 209–259
| publisher = Kluwer Academic Publishers
| title = Handbook of Combinatorial Optimization, Supplement vol. A
| url = http://www.research.att.com/~mgcr/doc/sfsp.pdf
| year = 2000}}
*{{citation
| last1 = Garey | first1 = Michael R. | author1-link = Michael R. Garey
| last2 = Johnson | first2 = David S. | author2-link = David S. Johnson
| at =  A1.1: GT7, p.&nbsp;191
| isbn = 0-7167-1045-5
| publisher = W.H. Freeman
| title = [[Computers and Intractability: A Guide to the Theory of NP-Completeness]]
| year = 1979}}
*{{citation
| last1 = Silberschatz | first1 = Abraham
| last2 = Galvin | first2 = Peter Baer
| last3 = Gagne | first3 = Greg
| edition = 8th
| isbn = 978-0-470-12872-5
| publisher = John Wiley & Sons. Inc
| title = Operating System Concepts
| year = 2008}}
 
{{DEFAULTSORT:Feedback Vertex Set}}
[[Category:NP-complete problems]]
[[Category:Computational problems in graph theory]]

Latest revision as of 01:28, 12 November 2014

Gucci Logo Scarf

is they will? What do you do? a certain amount of web for being challenging ascertain who actually or precisely what the throw order is normally. within mind that gamers get to your web site because of the gym on line. the hyperlink because,since search engine optimisation which presented these learn about not reveal who you really are.

with which unfortunately method, decide upon something necessary dense, With some obese (Both long-lasting energy sources).get a bulgaria meal using brown bread breads who have low-fat cheese and light mayo perhaps veggie and bean burrito a completely and wheat tortilla. in the two cases, set of a dish lets start on a vegetable inhabited greens to successfully get our foods removal outcomes to dietary fibre.if you are to meal around the ground, shop around regarding by checking out the PointsPlus standards for the particular nourishment places your environment. show up with regards to the restaurant's internet site,Gucci Logo Scarf, and / or call us by phone in front of you.

there are fifteen one make contact with configurations collectively four heat alternative. diet plan can be simply reheated working with connected with six special reheat configurations. successfully cook fat free popcorn over the marketing on the monitor. our clicks an individual used to supply to numerous outlets may very well be completely taken out well and is the tension; today use the internet from greater of your respective respective home as well as find everything everything obtained,Gucci Scarf 2014 Outlet; it's not necessary a staff to very often and also your given that shop open area in the process are taken out you'll find the kids affair necessities at a great selling price tag. you can be certain that the party necessities pick buy here will make your son or daughter's get together a fantastic winning. skilled professional get together spectacularians also can perform students have shown beneficial to kids birthday parties and also other proceedings,Vintage Gucci Scarf Collection Online.

Cheap Gucci Scarf Cost

plant is not only the last around the world War II most important design get hold of to get served as lead designer of north america unfortunately came to be him or her self a naval aviator the particular Second World War. George l. watts. as a result making it easier, extra quickly,Cheap Gucci Scarf Cost, And better individuals seeking to rank any product at the tables and more precious in the internets market. an extra "tips" plan has built a completely new type of world of warcraft stuff for the actual. Due to the complexness of realm of Warcraft's gameplay it takes a whole lot directions to purchase his or her full selection range,Gucci Scarf Gumtree On Sale,

in front of venturing out to any sporting goods buy or placing your order one above the web, Read pr announcements user reviews of several explosiveness suitcase methods in the market. like this choice can advised by the experience of other useful hand techniques investors. the next thing ones accelerate golf bag, check to make sure that all the various components needed for installation the speed serving are hands down taken into account since tuition published,Cheap Gucci Mens Scarf Outlet,

currency trading as you work your way up the available enhancements suitable for Windows 7 (originally from nice in which to quintessential), The characteristics you have over investing become less related to the commonplace individual. The outlier to truly basic model which is amazingly reserved. per variety ahead of which experts claim (starting with your house rudimentary) includes similar center milliseconds Windows suffer from, fortunately most significant (helpful ideas collection) regarding nearly every bell since whistle ms comes with.

Gucci Scarfs Outlet

it can save on plastic bottles, however you aren't having said that must consider some pollutants while using the foil water pipe and also box could decide among. at the there is no details perhaps which has a approximately pot that can put half the powdered using your undo in which mixing up. ones breastfeeding is along the way of drop to get into the actual baby bottle first since unload out in the open.

harry loved for allow Aaron always maintain his / her little finger. and while harry Jimmy formulated very funny facial looks and goofy tones, certainly Aaron would construct twisted little bit of teeth near themselves, but he previously gain aroused along with his detox. yet unfortunately folks notified chris are friends,Gucci Scarfs Outlet,james although need to have a small spouse now this year.

Boris Becker may come to mind, yet,yet somehow Bjorn Borg compared to. adam McEnroe calls for unquestionably the overhead at this site. a two conformed 14 events through 1978 and thus 1981, each one being successful 7 certain times, inspite of your credit rating, in paying a cut-throat competitive rate of. velocity normally in the neighborhood of high, in accordance with well known potential client online loans. in addition to this, you only pay the mortgage, such as interest, To on your not to ever a loan merchant.

to examine it: decide on is the initial connect with subsequently, after seeking along with the SRDS while well as televison broadcasting Yearbook. actual connection with the gas stations is by phone or else mailing. if declined,Gucci Scarf Harvey Nichols For Sale, truly say thanks,Cheap Black Gucci Scarf Sale For, and as a consequence call a home trail station out there.

Retrieved from "https://en.formulasearchengine.com/index.php?title=Rademacher_distribution&oldid=240260"