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Faster fixed parameter tractable algorithms for finding feedback vertex sets

2006
*
ACM Transactions on Algorithms
*

We also investigate the

doi:10.1145/1159892.1159898
fatcat:yr2r4tetjffbbcxh5ug5lmmvwq
*fixed**parameter*complexity of weighted*feedback**vertex**set*problem in weighted undirected graphs. ... A*feedback**vertex**set*(fvs) of a graph is a*set*of vertices whose removal results in an acyclic graph. ... Paulraja*for*fruitful discussions and comments on earlier drafts of the article, and Santosh Vempala*for*suggesting the direction*for*generalization in Theorem 3. ...##
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Faster Fixed Parameter Tractable Algorithms for Undirected Feedback Vertex Set
[chapter]

2002
*
Lecture Notes in Computer Science
*

We also investigate the

doi:10.1007/3-540-36136-7_22
fatcat:x3msdxladjfl7npwsi5zzxzn5y
*fixed**parameter*complexity of weighted*feedback**vertex**set*problem in weighted undirected graphs. ... A*feedback**vertex**set*(fvs) of a graph is a*set*of vertices whose removal results in an acyclic graph. ... Paulraja*for*fruitful discussions and comments on earlier drafts of the article, and Santosh Vempala*for*suggesting the direction*for*generalization in Theorem 3. ...##
###
New Races in Parameterized Algorithmics
[chapter]

2012
*
Lecture Notes in Computer Science
*

Once having classified an NP-hard problem

doi:10.1007/978-3-642-32589-2_2
fatcat:gpfsek5febh5rikaagecihqclq
*fixed*-*parameter**tractable*with respect to a certain*parameter*, the race*for*the most efficient*fixed*-*parameter**algorithm*starts. ... We discuss several of these aspects and particularly focus on the search*for*"stronger*parameterizations*" in developing*fixed*-*parameter**algorithms*. ... We thank André Nichterlein, Manuel Sorge, and Mathias Weller*for*their comments which have improved this article. ...##
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Parameterized Algorithmics for Graph Modification Problems: On Interactions with Heuristics
[chapter]

2016
*
Lecture Notes in Computer Science
*

We discuss several fruitful interactions between the development of

doi:10.1007/978-3-662-53174-7_1
fatcat:kegsdk75mncyhjecqz3ztmtffa
*fixed*-*parameter**algorithms*and the design of heuristics*for*graph modification problems, featuring quite different aspects of mutual ... Typically, graph modification problems are NP-hard, making them natural candidates*for**parameterized*complexity studies. ... We are grateful to Till Fluschnik and Vincent Froese*for**feedback*to our manuscript. ...##
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Parameterized Algorithmics for Graph Modification Problems: On Interactions with Heuristics
[article]

2016
*
arXiv
*
pre-print

We discuss several fruitful interactions between the development of

arXiv:1606.03268v1
fatcat:6ucc6vh32rfajofrbdsxtcpznq
*fixed*-*parameter**algorithms*and the design of heuristics*for*graph modification problems, featuring quite different aspects of mutual ... Typically, graph modification problems are NP-hard, making them natural candidates*for**parameterized*complexity studies. ... We are grateful to Till Fluschnik and Vincent Froese*for**feedback*to our manuscript. ...##
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Parameterizing above or below guaranteed values

2009
*
Journal of computer and system sciences (Print)
*

is

doi:10.1016/j.jcss.2008.08.004
fatcat:kxs4flhmengrxbougyjbwh4xla
*fixed*-*parameter**tractable*. ... We show that if we*parameterize*"sufficiently" above or below the tight bounds, then these*parameterized*versions are not*fixed*-*parameter**tractable*unless P = NP,*for*a subclass of NP-optimization problems ... We note that this problem is*fixed*-*parameter**tractable*by a*parameter*-preserving reduction to a weighted variant of Directed*Feedback**Vertex**Set*, where the vertices have weights and one has to decide whether ...##
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Fixed-parameter tractability results for feedback set problems in tournaments

2010
*
Journal of Discrete Algorithms
*

Using our

doi:10.1016/j.jda.2009.08.001
fatcat:qiuhaocrfrcp7aqsbcp3onvjd4
*parameterized**algorithm**for**Feedback**Vertex**Set*in tournaments, we also give an exact (not*parameterized*)*algorithm**for*it running in O (1.709 n ) time, where n is the number of input graph vertices ... We show that*Feedback**Vertex**Set*in tournaments (FVST) is amenable to the novel iterative compression technique, and we provide a depth-bounded search tree*for**Feedback*Arc*Set*in bipartite tournaments ... Following the same approach, we derive a*fixed*-*parameter**algorithm**for**Feedback*Arc*Set*in bipartite tournaments (FASBT). ...##
###
Fixed-Parameter Tractability Results for Feedback Set Problems in Tournaments
[chapter]

2006
*
Lecture Notes in Computer Science
*

Using our

doi:10.1007/11758471_31
fatcat:3uppqoabzjc37oyqe7tgl6rjre
*parameterized**algorithm**for**Feedback**Vertex**Set*in tournaments, we also give an exact (not*parameterized*)*algorithm**for*it running in O (1.709 n ) time, where n is the number of input graph vertices ... We show that*Feedback**Vertex**Set*in tournaments (FVST) is amenable to the novel iterative compression technique, and we provide a depth-bounded search tree*for**Feedback*Arc*Set*in bipartite tournaments ... Following the same approach, we derive a*fixed*-*parameter**algorithm**for**Feedback*Arc*Set*in bipartite tournaments (FASBT). ...##
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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. ... [66] to develop a (non-*parameterized*)*faster**algorithm**for*this problem. ...##
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On tractable cases of Target Set Selection

2012
*
Social Network Analysis and Mining
*

TSS can be efficiently solved on graphs with small

doi:10.1007/s13278-012-0067-7
fatcat:k2q4nk4qnbatnemcvpvm32tqjq
*feedback*edge*set*number and also turns out to be*fixed*-*parameter**tractable*when*parameterized*by the*vertex*cover number, both results contrasting known ... While these*tractability*results are relevant*for*sparse networks, we also show efficient*fixed*-*parameter**algorithms**for*the*parameter*cluster edge deletion number, yielding*tractability**for*certain dense ... Like the*vertex*cover number τ , the*feedback*edge*set*number f is a "weaker"*parameter*than treewidth, raising hope*for**faster**algorithms**for*TSS in cases where f is small. ...##
###
On Tractable Cases of Target Set Selection
[chapter]

2010
*
Lecture Notes in Computer Science
*

TSS can be efficiently solved on graphs with small

doi:10.1007/978-3-642-17517-6_34
fatcat:utuzuybyojah5iljtjbk3j2cuq
*feedback*edge*set*number and also turns out to be*fixed*-*parameter**tractable*when*parameterized*by the*vertex*cover number, both results contrasting known ... While these*tractability*results are relevant*for*sparse networks, we also show efficient*fixed*-*parameter**algorithms**for*the*parameter*cluster edge deletion number, yielding*tractability**for*certain dense ... Like the*vertex*cover number τ , the*feedback*edge*set*number f is a "weaker"*parameter*than treewidth, raising hope*for**faster**algorithms**for*TSS in cases where f is small. ...##
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Some Parameterized Problems On Digraphs

2007
*
Computer journal
*

The problems include the

doi:10.1093/comjnl/bxm039
fatcat:5yqonwpu2jgqfkuv7itpc7j3km
*feedback**vertex*and arc*set*problems, induced subdigraph problems and directed k-leaf problems. We also prove some new results on the topic. ... We survey results and open questions on complexity of*parameterized*problems on digraphs. ... Acknowledgements We are thankful to the referee*for*several important suggestions and*for*proving us with [48] . Research of both authors was supported in part by an EPSRC grant. ...##
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Extended MSO Model Checking via Small Vertex Integrity
[article]

2022
*
arXiv
*
pre-print

We show that the problem is

arXiv:2202.08445v3
fatcat:whndbaukenasjjdprpfqlwsc5q
*fixed*-*parameter**tractable**parameterized*by*vertex*integrity, where*vertex*integrity is a graph*parameter*standing between*vertex*cover number and treedepth. ... Our result thus narrows the gap between the*fixed*-*parameter**tractability**parameterized*by*vertex*cover number and the W[1]-hardness*parameterized*by treedepth. ... Acknowledgements The authors thank Michael Lampis and Valia Mitsou*for*fruitful discussions and sharing a preliminary version of [45] . ...##
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A fixed-parameter algorithm for the directed feedback vertex set problem

2008
*
Journal of the ACM
*

The (

doi:10.1145/1411509.1411511
fatcat:lxicbc7f3bgldllq7ubcjuui6y
*parameterized*)*feedback**vertex**set*problem on directed graphs, which we refer to as the dfvs problem, is defined as follows: given a directed graph G and a*parameter*k, either construct a*feedback*... In this paper we develop new*algorithmic*techniques that result in an*algorithm*with running time 4 k k!n O(1)*for*the dfvs problem, thus showing that this problem is*fixed*-*parameter**tractable*. ... In the last three years, the use of iterative compression facilitated the resolution of the status of*fixed**parameter**tractability*, and the design of*faster**parameterized**algorithms*,*for*a number of problems ...##
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A fixed-parameter algorithm for the directed feedback vertex set problem

2008
*
Proceedings of the fourtieth annual ACM symposium on Theory of computing - STOC 08
*

The (

doi:10.1145/1374376.1374404
dblp:conf/stoc/ChenLL08
fatcat:akj3qzdb75apjc3n3uk7ixu5au
*parameterized*)*feedback**vertex**set*problem on directed graphs, which we refer to as the dfvs problem, is defined as follows: given a directed graph G and a*parameter*k, either construct a*feedback*... In this paper we develop new*algorithmic*techniques that result in an*algorithm*with running time 4 k k!n O(1)*for*the dfvs problem, thus showing that this problem is*fixed*-*parameter**tractable*. ... In the last three years, the use of iterative compression facilitated the resolution of the status of*fixed**parameter**tractability*, and the design of*faster**parameterized**algorithms*,*for*a number of problems ...
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