Some Parameterized Problems On Digraphs

Gutin, Gregory; Yeo, Anders

doi:10.1093/comjnl/bxm039

Cited by 20 publications

(19 citation statements)

References 46 publications

(39 reference statements)

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“…After numerous efforts, however, the problem remained open. In the past 15 years, the problem has been constantly and explicitly posted as an open problem in a large number of publications in the literature (see, for example, [7,8,9,10,11,16,17,18,20,26,27,28]). The problem has become a well-known and outstanding open problem in parameterized computation and complexity.…”

Section: Introductionmentioning

confidence: 99%

A fixed-parameter algorithm for the directed feedback vertex set problem

Chen

Liu

et al. 2008

Proceedings of the Fortieth Annual ACM Symposium on Theory of Computing

121

162

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The (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 vertex set of at most k vertices in G or report that no such set exists. Whether or not the dfvs problem is fixed-parameter tractable has been a well-known open problem in parameterized computation and complexity, i.e., whether the problem can be solved in time f (k)n O(1) for some function f . 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.

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Section: Introductionmentioning

confidence: 99%

A fixed-parameter algorithm for the directed feedback vertex set problem

Chen

Liu

et al. 2008

Proceedings of the Fortieth Annual ACM Symposium on Theory of Computing

121

162

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“…They have also established a min-max theorem for FVS in bipartite tournaments. Concerning FAS in bipartite tournaments, Gutin and Yeo [9] note that it is fixedparameter tractable, that is, the exponential part of the running time can be restricted to the parameter k, the We close this gap here by showing that FAS is indeed NP-complete in bipartite tournaments. To this end, we give a polynomial-time many-one reduction from the CNF SATISFIABILITY (CNF-SAT) problem.…”

mentioning

confidence: 84%

Feedback arc set in bipartite tournaments is NP-complete

Guo

Hüffner

Moser

2007

Information Processing Letters

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“…However, the parametrized complexity of k-FVS and k-FAS was a well known open problem in the area for more than a decade. We refer to the survey of Gutin and Yeo [30] for the history of these problems prior to its solution by Chen et al [13] who obtained an algorithm with running time 2 O(k log k) n O (1) . The running time of this algorithm has not yet been improved and finding an algorithm with running time 2 O(k) n O(1) remains a challenging open problem.…”

Section: Introductionmentioning

confidence: 99%

Algorithms and Kernels for Feedback Set Problems in Generalizations of Tournaments

2015

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In the Directed Feedback Arc (Vertex) Set problem, we are given a digraph D with vertex set V (D) and arcs set A(D) and a positive integer k, and the question is whether there is a subset X of arcs (vertices) of size at most k such that the digraph obtained after deleting X from D is an acyclic digraph. In this paper we study these two problems in the realm of parametrized and kernelization complexity. More precisely, for these problems we give polynomial time algorithms, known as kernelization algorithms, on several digraph classes that given an instance (D, k) of the problem returns an equivalent instance (D , k ) such that the size of D and k is at most k O(1) . We extend previous results for Directed Feedback Arc (Vertex) Set on tournaments to much larger and well studied classes of digraphs. Specifically we obtain polynomial kernels for k-FVS on digraphs with bounded independence number, locally semicomplete digraphs and some totally -decomposable digraphs, including quasi-transitive digraphs. We also obtain polynomial kernels for k-FAS on some totally -decomposable digraphs, including quasi-transitive digraphs. Finally, 123 Algorithmica we design a subexponential algorithm for k-FAS running in time 2 O( √ k(log k) c ) n d for constants c, d. on locally semicomplete digraphs.

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Some Parameterized Problems On Digraphs

Cited by 20 publications

References 46 publications

A fixed-parameter algorithm for the directed feedback vertex set problem

A fixed-parameter algorithm for the directed feedback vertex set problem

Feedback arc set in bipartite tournaments is NP-complete

Algorithms and Kernels for Feedback Set Problems in Generalizations of Tournaments

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