Fixed-Parameter Tractability Results for Feedback Set Problems in Tournaments

Dom, Michael; Guo, Jiong; Hüffner, Falk; Niedermeier, Rolf; Truss, Anke

doi:10.1007/11758471_31

Cited by 43 publications

(53 citation statements)

References 15 publications

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“…The revised lemma for T 3 3 now reads as follows, where the recurrences are listed according to the sequence they appear; they correspond to (4), (8), and (12). Notice that the first and the third equations were neglected by the earlier analysis, since they were already covered by worse cases in the former "star analysis."…”

Section: Solving the Recurrence Equationsmentioning

confidence: 99%

“…(b) According to the revised heuristic priorities, (12) arose. We try to cope with these situations in the next section.…”

Section: Solving the Recurrence Equationsmentioning

confidence: 99%

“…Upon designing fixed-parameter algorithms for feedback set problems in tournaments, our algorithm can be used in some cases, see [12]. • Computational biology: Downey, Fellows and Stege [13] mention that the MAXI-MUM AGREEMENT SUBTREE problem can be solved with the help of 3HS.…”

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confidence: 99%

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A Top-Down Approach to Search-Trees: Improved Algorithmics for 3-Hitting Set

Fernau

2008

Algorithmica

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In this paper, we show how to systematically improve on parameterized algorithms and their analysis, focusing on search-tree based algorithms for 3-HITTING SET. We concentrate on algorithms which are easy to implement, in contrast with the highly sophisticated algorithms which have been designed previously to improve on the exponential base in the algorithms.However, this necessitates a more complex algorithm analysis based on a so-called auxiliary parameter, a technique which we believe can be used in other circumstances, as well.

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Section: Solving the Recurrence Equationsmentioning

confidence: 99%

“…(b) According to the revised heuristic priorities, (12) arose. We try to cope with these situations in the next section.…”

Section: Solving the Recurrence Equationsmentioning

confidence: 99%

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A Top-Down Approach to Search-Trees: Improved Algorithmics for 3-Hitting Set

Fernau

2008

Algorithmica

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“…It is known that k-FVS problem is solvable in time 2 k n O(1) on tournaments [18] and bipartite tournaments (orientation of a undirected complete bipartite graph) [31] with n vertices. Moreover, the weighted version of this problem admits a c k n O(1) time algorithm on tournaments [40].…”

Section: Introductionmentioning

confidence: 99%

“…Later this algorithm has been improved to 2 O( √ k) n O (1) [21,24,36]. On the kernelization front, Dom et al [18] gave an O(k 3 ) kernel for k-FVS on tournaments by a reduction to 3-Hitting Set. Recently Abu-Khzam [1] designed an O(k d−1 ) kernel for the dHitting Set, implying the existence of an O(k 2α ) kernel for k-FVS on digraphs with independence number at most α.…”

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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Feedback Vertex Sets in Tournaments

Gaspers

Mnich

2012

Journal of Graph Theory

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We study combinatorial and algorithmic questions around minimal feedback vertex sets in tournament graphs.On the combinatorial side, we derive strong upper and lower bounds on the maximum number of minimal feedback vertex sets in an n-vertex tournament. We prove that every tournament on n vertices has at most 1.6740 n minimal feedback vertex sets and that there is an infinite family of tournaments, all having at least 1.5448 n minimal feedback vertex sets. This improves and extends the bounds of Moon (1971).On the algorithmic side, we design the first polynomial space algorithm that enumerates the minimal feedback vertex sets of a tournament with polynomial delay. The combination of our results yields the fastest known algorithm for finding a minimum size feedback vertex set in a tournament.

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Fixed-Parameter Tractability Results for Feedback Set Problems in Tournaments

Cited by 43 publications

References 15 publications

A Top-Down Approach to Search-Trees: Improved Algorithmics for 3-Hitting Set

A Top-Down Approach to Search-Trees: Improved Algorithmics for 3-Hitting Set

Algorithms and Kernels for Feedback Set Problems in Generalizations of Tournaments

Feedback Vertex Sets in Tournaments

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