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

Chen, Jianer; Liu, Yang; Lu, Songjian; O’Sullivan, Barry; Razgon, Igor

doi:10.1145/1374376.1374404

Cited by 121 publications

(167 citation statements)

References 33 publications

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“…If there is a dirty triple {a, b, c} forming three dirty pairs contained in D, namely, {a, b}, {b, c}, {a, c} ∈ D, then remove these three pairs from D. Branch into all six possible orders of a, b, and c. In each subcase, if the corresponding order is not consistent with L, discard this subcase, otherwise, add the corresponding order to L and decrease the parameter according to this subcase. The worst-case branching vector of this case is (3,4,4,5,5,6), giving a branching number 1.52. To see this, note that we only consider instances with at least three votes, since Kemeny Score is polynomial-time solvable for only two votes.…”

Section: Search Tree Algorithmmentioning

confidence: 99%

Fixed-Parameter Algorithms for Kemeny Scores

Betzler

Fellows

Guo

et al.

Lecture Notes in Computer Science

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Abstract. The Kemeny Score problem is central to many applications in the context of rank aggregation. Given a set of permutations (votes) over a set of candidates, one searches for a "consensus permutation" that is "closest" to the given set of permutations. Computing an optimal consensus permutation is NP-hard. We provide first, encouraging fixed-parameter tractability results for computing optimal scores (that is, the overall distance of an optimal consensus permutation). Our fixedparameter algorithms employ the parameters "score of the consensus", "maximum distance between two input permutations", and "number of candidates". We extend our results to votes with ties and incomplete votes, thus, in both cases having no longer permutations as input.

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Section: Search Tree Algorithmmentioning

confidence: 99%

Fixed-Parameter Algorithms for Kemeny Scores

Betzler

Fellows

Guo

et al.

Lecture Notes in Computer Science

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“…It is shown in Chen et al (2008) that FeedbackVertexSet for directed graphs is fixed-parameter tractable. The authors provide an algorithm which solves…”

Section: Addtaxa Hgt (N K) Is Yes If and Only If The Answer Tomentioning

confidence: 99%

“…This number is less than the number of reticulation vertices and we would expect this latter number to be much less than the size of N . Consequently, k may typically be relatively small and so the algorithm in Chen et al (2008) should work well in helping to find the solution for many instances of AddTaxa(N , k).…”

Section: Addtaxa Hgt (N K) Is Yes If and Only If The Answer Tomentioning

confidence: 99%

Analyzing and reconstructing reticulation networks under timing constraints

2009

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Reticulation networks are now frequently used to model the history of life for various groups of species whose evolutionary past is likely to include reticulation events such as horizontal gene transfer or hybridization. However, the reconstructed networks are rarely guaranteed to be temporal. If a reticulation network is temporal, then it satisfies the two biologically motivated timing constraints of instantaneously occurring reticulation events and successively occurring speciation events. On the other hand, if a reticulation network is not temporal, it is always possible to make it temporal by adding a number of additional unsampled or extinct taxa. In the first half of the paper, we show that deciding whether a given number of additional taxa is sufficient to transform a non-temporal reticulation network into a temporal one is an NP-complete problem. As one is often given a set of gene trees instead of a network in the context of hybridization, this motivates the second half of the paper which provides an algorithm, called TemporalHybrid, for reconstructing a temporal hybridization network that simultaneously explains the ancestral history of two trees or indicates that no such network exists. We further derive two methods to decide whether or not a temporal hybridization network exists for two given trees and illustrate one of the methods on a grass data set.All authors contributed equally to this work.

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“…The search for a polynomial kernel for FVS lead to surprising applications of deep combinatorial results such as Gallai's theorem [26], which has also been found useful in designing FPT algorithms [10]. While investigating the graph cut problems such as MWC, Márx [21] introduced the important separator technique, which turned out to be very robust and is now the key ingredient in parameterized algorithms for various problems such as variants of FVS [5,10] or Almost 2-SAT [24]. Moreover, the recent developments on MWC show applicability of linear programming in parameterized complexity, leading to the fastest currently known algorithms not only for MWC, but also Almost 2-SAT and OCT [9,22].…”

Section: Introductionmentioning

confidence: 99%

On Group Feedback Vertex Set Parameterized by the Size of the Cutset

Cygan

Pilipczuk

2014

Algorithmica

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Copies of full items can be used for personal research or study, educational, or not-forprofit purposes without prior permission or charge. Provided that the authors, title and full bibliographic details are credited, a hyperlink and/or URL is given for the original metadata page and the content is not changed in any way. Publisher statement:The final publication is available at Springer via http://dx.doi.org/10.1007/s00453-014-9966-5 A note on versions:The version presented here may differ from the published version or, version of record, if you wish to cite this item you are advised to consult the publisher's version. Please see the 'permanent WRAP url' above for details on accessing the published version and note that access may require a subscription. Abstract We study parameterized complexity of a generalization of the classical Feedback Vertex Set problem, namely the Group Feedback Vertex Set problem: we are given a graph G with edges labeled with group elements, and the goal is to compute the smallest set of vertices that hits all cycles of G that evaluate to a non-null element of the group. This problem generalizes not only Feedback Vertex Set, but also Subset Feedback Vertex Set, Multiway Cut and Odd Cycle Transversal. Completing the results of Guillemot [Discr. Opt. 2011], we provide a fixed-parameter algorithm for the parameterization by the size of the cutset only. Our algorithm works even if the group is given as a blackbox performing group operations.A preliminary version of this paper has been presented at WG 2012 [8].

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

Cited by 121 publications

References 33 publications

Fixed-Parameter Algorithms for Kemeny Scores

Fixed-Parameter Algorithms for Kemeny Scores

Analyzing and reconstructing reticulation networks under timing constraints

On Group Feedback Vertex Set Parameterized by the Size of the Cutset

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