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

Cygan, Marek; Pilipczuk, Marcin; Pilipczuk, Michał

doi:10.1007/s00453-014-9966-5

Cited by 8 publications

(2 citation statements)

References 27 publications

(32 reference statements)

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“…Guillemot [17] was the first to study GFVS in terms of parameterized complexity, and showed FPT algorithms parameterized by k + |Γ|. Cygan et al [11] showed GFVS to be FPT parameterized by k alone, even when the group is given only implicitly by an oracle supporting group operations. Iwata et al [22] showed a faster algorithm, solving GFVS in time O * (4 k ) using an LP-branching approach, also in the oracle model.…”

Section: Questionmentioning

confidence: 99%

Almost Consistent Systems of Linear Equations

Dabrowski¹,

Jönsson²,

Wang³

et al. 2023

Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)

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Checking whether a system of linear equations is consistent is a basic computational problem with ubiquitous applications. When dealing with inconsistent systems, one may seek an assignment that minimizes the number of unsatisfied equations. This problem is NP-hard and UGC-hard to approximate within any constant even for two-variable equations over the two-element field. We study this problem from the point of view of parameterized complexity, with the parameter being the number of unsatisfied equations. We consider equations defined over Euclidean domains-a family of commutative rings that generalize finite and infinite fields including the rationals, the ring of integers and many other structures. We show that if every equation contains at most two variables, the problem is fixed-parameter tractable. This generalizes many eminent graph separation problems such as Bipartization, Multiway Cut and Multicut parameterized by the size of the cutset. To complement this, we show that the problem is W[1]-hard when three or more variables are allowed in an equation, as well as for many commutative rings that are not Euclidean domains. On the technical side, we introduce the notion of important balanced subgraphs, generalizing important separators of Marx [Theor. Comput. Sci. 2006] to the setting of biased graphs. Furthermore, we use recent results on parameterized MinCSP [Kim et al., SODA 2021] to efficiently solve a generalization of Multicut with disjunctive cut requests.

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Section: Questionmentioning

confidence: 99%

Almost Consistent Systems of Linear Equations

Dabrowski¹,

Jönsson²,

Wang³

et al. 2023

Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)

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“…At the same time, many variants of FVS received significant attention, including Subset FVS [10,16,21], Group FVS [9,13,16,19], Connected FVS [23], or Simultaneous FVS [3].…”

Section: Introductionmentioning

confidence: 99%

An Improved FPT Algorithm for Independent Feedback Vertex Set

Pilipczuk

2020

Theory Comput Syst

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We study the Independent Feedback Vertex Set problem -a variant of the classic Feedback Vertex Set problem where, given a graph G and an integer k, the problem is to decide whether there exists a vertex set S ⊆ V (G) such that G \ S is a forest and S is an independent set of size at most k. We present an O * ((1 + ϕ 2 ) k )-time FPT algorithm for this problem, where ϕ < 1.619 is the golden ratio, improving the previous fastest O * (4.1481 k )-time algorithm given by Agrawal et al. [2]. The exponential factor in our time complexity bound matches the fastest deterministic FPT algorithm for the classic Feedback Vertex Set problem.On the technical side, the main novelty is a refined measure of an input instance in a branching process, that allows for a simpler and more concise description and analysis of the algorithm. .pl. 1 The O * -notation suppresses factors that are polynomial in the input size. 2 Actually in the randomized FPT algorithm for FVS, the parameter is the treewidth of the graph. Since the treewidth of a yes-instance (G, k) to FVS is at most k + 1, the randomized algorithm for FVS runs in time O * (3 k ).

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An Improved FPT Algorithm for Independent Feedback Vertex Set

Pilipczuk

2018

Graph-Theoretic Concepts in Computer Science

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

Cited by 8 publications

References 27 publications

Almost Consistent Systems of Linear Equations

Almost Consistent Systems of Linear Equations

An Improved FPT Algorithm for Independent Feedback Vertex Set

An Improved FPT Algorithm for Independent Feedback Vertex Set

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