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Compression-based fixed-parameter algorithms for feedback vertex set and edge bipartization

2006
*
Journal of computer and system sciences (Print)
*

Here, m denotes the number of graph

doi:10.1016/j.jcss.2006.02.001
fatcat:aoxbedbjmnd2jged7hlbc7xmma
*edges*, k denotes the size of the*feedback**vertex**set*searched*for*,*and*c is a constant. ... As a further result, we present a*fixed*-*parameter**algorithm*with runtime O(2 k · m 2 )*for*the NP-complete*EDGE**BIPARTIZATION*problem, which asks*for*at most k*edges*to remove from a graph to make it bipartite ... Acknowledgments The authors thank the anonymous referees of WADS 2005*for*helpful*and*inspiring comments*and*an anonymous referee of the Journal of Computer*and*System Sciences*for*helping to improve the ...##
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Improved Fixed-Parameter Algorithms for Two Feedback Set Problems
[chapter]

2005
*
Lecture Notes in Computer Science
*

of the

doi:10.1007/11534273_15
fatcat:hxjgozqbdzg4vbpwxesls2riuy
*feedback**vertex**set*searched*for*,*and*c is a constant. ... As a second result, we present a*fixed*-*parameter**algorithm**for*the NPcomplete*Edge**Bipartization*problem with runtime O(2 k · m 2 ). ... The authors would like to thank the anonymous referees of WADS 2005*for*helpful*and*inspiring comments. ...##
###
Iterative Compression for Exactly Solving NP-Hard Minimization Problems
[chapter]

2009
*
Lecture Notes in Computer Science
*

We describe several

doi:10.1007/978-3-642-02094-0_4
fatcat:ley2ifkrxbcw7bhzrktb5ijawq
*algorithmic*results*based*on iterative*compression**and*point out some challenges*for*future research. ... This technique has proven very useful*for*achieving a number of recent breakthroughs in the development of*fixed*-*parameter**algorithms**for*NP-hard minimization problems. ... Acknowledgement: We are grateful to Christian Komusiewicz, Matthias Müller-Hannemann,*and*Siavash Vahdati Daneshmand*for*constructive comments improving the presentation of this paper. ...##
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Techniques for Practical Fixed-Parameter Algorithms

2007
*
Computer journal
*

The

doi:10.1093/comjnl/bxm040
fatcat:jbffitiefzfexftg3lgl7xnsza
*fixed*-*parameter*approach is an*algorithm*design technique*for*solving combinatorially hard (mostly NP-hard) problems. ...*For*some of these problems, it can lead to*algorithms*that are both efficient*and*yet at the same time guaranteed to find optimal solutions. ... Being the only*fixed*-*parameter**algorithm*known*for**EDGE**BIPARTIZATION*, this*algorithm*is similar to the iterative*compression**algorithm*that Reed et al. ...##
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Compression via Matroids: A Randomized Polynomial Kernel for Odd Cycle Transversal
[article]

2011
*
arXiv
*
pre-print

In a breakthrough result Reed, Smith,

arXiv:1107.3068v2
fatcat:7xivak7xhvbgnmpazcgr2kdvlq
*and*Vetta (Operations Research Letters, 2004) gave a (4^kkmn) time*algorithm**for*it, the first*algorithm*with polynomial runtime of uniform degree*for*every*fixed*...*For*OCT, the matroid is built to allow us to simulate the computation of the iterative*compression*step of the*algorithm*of Reed, Smith,*and*Vetta, applied (*for*only one round) to an approximate odd cycle ...*for**Feedback**Vertex**Set**and*Odd Cycle Transversal. ...##
###
Algorithm Engineering for Optimal Graph Bipartization

2009
*
Journal of Graph Algorithms and Applications
*

We examine exact

doi:10.7155/jgaa.00177
fatcat:4lrmvfxhcndsfjtajfcql2hyme
*algorithms**for*the NP-hard Graph*Bipartization*problem. The task is, given a graph, to find a minimum*set*of vertices to delete to make it bipartite. ...*Based*on the "iterative*compression*" method introduced by Reed, Smith,*and*Vetta in 2004, we present new*algorithms**and*experimental results. The worst-case time complexity is improved. ... Acknowledgments The author is grateful to Jens Gramm (Tübingen)*and*Jiong Guo, Rolf Niedermeier,*and*Sebastian Wernicke (Jena)*for*many helpful suggestions. ...##
###
Algorithm Engineering for Optimal Graph Bipartization
[chapter]

2005
*
Lecture Notes in Computer Science
*

We examine exact

doi:10.1007/11427186_22
fatcat:qzxhojrswrf45ks4zntpoacnsm
*algorithms**for*the NP-hard Graph*Bipartization*problem. The task is, given a graph, to find a minimum*set*of vertices to delete to make it bipartite. ...*Based*on the "iterative*compression*" method introduced by Reed, Smith,*and*Vetta in 2004, we present new*algorithms**and*experimental results. The worst-case time complexity is improved. ... Acknowledgments The author is grateful to Jens Gramm (Tübingen)*and*Jiong Guo, Rolf Niedermeier,*and*Sebastian Wernicke (Jena)*for*many helpful suggestions. JGAA, 13(2) 77-98 (2009) 95 ...##
###
Experimental Evaluation of Parameterized Algorithms for Feedback Vertex Set

2018
*
Symposium on Experimental and Efficient Algorithms
*

In this paper we provide an exhaustive experimental evaluation of

doi:10.4230/lipics.sea.2018.12
dblp:conf/wea/KiljanP18
fatcat:symgz3xuzfffzphp5jkzox3qwy
*fixed*-*parameter**and*branching*algorithms**for**Feedback**Vertex**Set*. ... From the point of view of*parameterized**algorithms**and**fixed*-*parameter*tractability,*Feedback**Vertex**Set*is one of the landmark problems: a long line of study resulted in multiple*algorithmic*approaches ... Conclusions We have conducted a thorough experimental evaluation of various*parameterized**algorithms**for*the*Feedback**Vertex**Set*problem, following the setup of*Parameterized**Algorithms**and*Computational ...##
###
Simpler Parameterized Algorithm for OCT
[chapter]

2009
*
Lecture Notes in Computer Science
*

We give a simple

doi:10.1007/978-3-642-10217-2_37
fatcat:sifiew6vt5gbhbpslmtflzv6ue
*and*intuitive*fixed**parameter*tractable*algorithm**for*the Odd Cycle Transversal problem, running in time O(3 k · k · |E| · |V |). ... Our*algorithm*is best viewed as a reinterpretation of the classical Iterative*Compression**algorithm**for*Odd Cycle Transversal by Reed, Smith*and*Vetta [8] . ... Fomin, Rolf Niedermeier, Venkatesh Raman*and*Frances Rosamond*for*helpful discussions*and**for*suggesting to put this article in print. ...##
###
A Complexity Dichotomy for Finding Disjoint Solutions of Vertex Deletion Problems
[chapter]

2009
*
Lecture Notes in Computer Science
*

This class includes problems such as

doi:10.1007/978-3-642-03816-7_28
fatcat:3gifzkyfkbaw3gvaedx5cynmda
*Vertex*Cover (here the corresponding*compression*task is decidable in polynomial time) or Undirected*Feedback**Vertex**Set*(here the corresponding*compression*task is ... We consider a large class of*vertex*deletion problems on undirected graphs*and*show that, except*for*few cases which are polynomial-time solvable, the others are NP-complete. ...*For*instance, the*fixed*-*parameter*tractability results (using iterative*compression*)*for**Vertex**Bipartization*[17] or Undirected*Feedback**Vertex**Set*[3, 5, 8] leave open whether the respective*Compression*...##
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A Complexity Dichotomy for Finding Disjoint Solutions of Vertex Deletion Problems

2011
*
ACM Transactions on Computation Theory
*

This class includes problems such as

doi:10.1145/1944857.1944860
fatcat:ci3bfpo4r5bulg3g4t4y2n2xly
*Vertex*Cover (here the corresponding*compression*task is decidable in polynomial time) or Undirected*Feedback**Vertex**Set*(here the corresponding*compression*task is ... We consider a large class of*vertex*deletion problems on undirected graphs*and*show that, except*for*few cases which are polynomial-time solvable, the others are NP-complete. ...*For*instance, the*fixed*-*parameter*tractability results (using iterative*compression*)*for**Vertex**Bipartization*[17] or Undirected*Feedback**Vertex**Set*[3, 5, 8] leave open whether the respective*Compression*...##
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A survey of parameterized algorithms and the complexity of edge modification
[article]

2020
*
arXiv
*
pre-print

The survey provides an overview of the developing area of

arXiv:2001.06867v2
fatcat:6ogysat6n5drpbxsvs63zjmega
*parameterized**algorithms**for*graph modification problems. ... We concentrate on*edge*modification problems, where the task is to change a small number of adjacencies in a graph in order to satisfy some required property. ... We thank Marcin Pilipczuk, William Lochet,*and*Dekel Tsur*for*helpful comments. References ...##
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Iterative compression and exact algorithms

2010
*
Theoretical Computer Science
*

We exemplify our findings with

doi:10.1016/j.tcs.2009.11.012
fatcat:xgs4a57pcbhhnkqrmlg3l2eata
*algorithms**for*the Maximum Independent*Set*problem, a*parameterized**and*a counting version of d-Hitting*Set**and*the Maximum Induced Cluster Subgraph problem. ... Iterative*Compression*has recently led to a number of breakthroughs in*parameterized*complexity. ... The authors are grateful to an anonymous referee*for*many suggestions helping us to improve the presentation of the paper. ...##
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Linear Time Parameterized Algorithms via Skew-Symmetric Multicuts
[article]

2013
*
arXiv
*
pre-print

Using our

arXiv:1304.7505v1
fatcat:bzafkg6glzahxl2jy7pzsfxttu
*algorithm*, we show that Almost 2-SAT has an*algorithm*with running time O(4^kk^4ℓ)*and*we obtain*algorithms**for*Odd Cycle Transversal*and**Edge**Bipartization*which run in time O(4^kk^4(m+n))*and*... This gives the first*fixed*-*parameter*tractable*algorithm**for*this problem answering a question posed in a paper by a superset of the authors [STACS, 2013]. ... Using a known linear time*parameter*preserving reduction from*Edge**Bipartization*to OCT, we also get a similar result*for**Edge**Bipartization*. ...##
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Representative sets and irrelevant vertices: New tools for kernelization
[article]

2012
*
arXiv
*
pre-print

*For*a directed graph G=(V,E)

*and*

*sets*S, T ⊆ V, let r be the size of a minimum (S,T)-

*vertex*cut (which may intersect S

*and*T). ... We can find a

*set*Z ⊆ V of size O(|S|*|T|*r) which contains a minimum (A,B)-

*vertex*cut

*for*every A ⊆ S, B ⊆ T. ... The authors are grateful to Dániel Marx

*for*comments on an early draft of the paper,

*and*to Saket Saurabh

*for*an early version of [32] . ...

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