W-Hierarchies Defined by Symmetric Gates

Fellows, Michael R.; Flum, Jörg; Hermelin, Danny; Müller, Moritz; Rosamond, Frances A.

doi:10.1007/s00224-008-9138-6

Cited by 7 publications

(5 citation statements)

References 11 publications

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“…In Section 5, we suggest an enhanced weft hierarchy called counting weft hierarchy dedicated to those cardinality-constrained problems, such as max sat-k and max k-set cover which are W[i]-hard for some i, and in W[P], but not even known to be in W[j] for some integer j. Related issues have been discussed by Fellows et al [20].…”

Section: Preliminariesmentioning

confidence: 99%

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Parameterized exact and approximation algorithms for maximumk-set cover and related satisfiability problems

Bonnet

Paschos

Sikora

2016

RAIRO-Theor. Inf. Appl.

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Given a family of subsets S over a set of elements X and two integers p and k, max k-set cover consists of finding a subfamily T ⊆ S of cardinality at most k, covering at least p elements of X. This problem is W[2]-hard when parameterized by k, and FPT when parameterized by p. We investigate the parameterized approximability of the problem with respect to parameters k and p. Then, we show that max sat-k, a satisfiability problem generalizing max k-set cover, is also FPT with respect to parameter p.

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Section: Preliminariesmentioning

confidence: 99%

“…As mentioned in the introduction, the results by Fellows et al [20] which also focus on parallel W-hierarchy with other types of vertices, cannot be used here since the counting vertices are symmetric but not bounded.…”

Section: Some Preliminary Thoughts About An Enhanced Weft Hierarchy: mentioning

confidence: 99%

Parameterized exact and approximation algorithms for maximumk-set cover and related satisfiability problems

Bonnet

Paschos

Sikora

2016

RAIRO-Theor. Inf. Appl.

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“…Modifying the set of allowed gates in WCS(t,d) dramatically simplifies the task of finding a membership proof but it may lead to a slightly different W-hierarchy: For instance, we can show that MajAB can be reduced to a WCS(2,d) problem variant, where instead of NOT, AND, or OR gates, majority gates (which output TRUE if the majority of inputs is TRUE) are used. This version of the problem which we call WCS(t,d)(Maj), and the corresponding W(Maj)-hierarchy have been studied by Fellows et al [63]. While W…”

Section: W-hierarchy and Majority-based Problemsmentioning

confidence: 99%

“…Besides majority variants of Set Cover and Hitting Set (see [63,Sec. 7]) promising natural candidates like MajAB for W [2](Maj)-complete problems may occur in the context of computational social choice, where majority-based properties such as Condorcet winner frequently occur.…”

Section: Key Questionmentioning

confidence: 99%

Parameterized algorithmics for computational social choice: Nine research challenges

Bredereck

Chen

Faliszewski³

et al. 2014

Tinshhua Sci. Technol.

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Computational Social Choice is an interdisciplinary research area involving Economics, Political Science, and Social Science on the one side, and Mathematics and Computer Science (including Artificial Intelligence and Multiagent Systems) on the other side. Typical computational problems studied in this field include the vulnerability of voting procedures against attacks, or preference aggregation in multi-agent systems. Parameterized Algorithmics is a subfield of Theoretical Computer Science seeking to exploit meaningful problemspecific parameters in order to identify tractable special cases of in general computationally hard problems. In this paper, we propose nine of our favorite research challenges concerning the parameterized complexity of problems appearing in this context.

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“…It might be W [2]-complete, but all we currently know is that it is contained in W [2] (Maj), a class presumably larger than W[2] [17].…”

Section: Open Questions and Conclusionmentioning

confidence: 99%

How to Put through Your Agenda in Collective Binary Decisions

Alon

Bredereck

Kratsch

et al. 2013

Algorithmic Decision Theory

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Abstract. We consider the following decision scenario: a society of voters has to find an agreement on a set of proposals, and every single proposal is to be accepted or rejected. Each voter supports a certain subset of the proposals-the favorite ballot of this voter-and opposes the remaining ones. He accepts a ballot if he supports more than half of the proposals in this ballot. The task is to decide whether there exists a ballot approving a set of selected proposals (agenda) such that all voters (or a strict majority of them) accept this ballot. On the negative side both problems are NP-complete, and on the positive side they are fixed-parameter tractable with respect to the total number of proposals or with respect to the total number of voters. We look into further natural parameters and study their influence on the computational complexity of both problems, thereby providing both tractability and intractability results. Furthermore, we provide tight combinatorial bounds on the worst-case size of an accepted ballot in terms of the number of voters.

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W-Hierarchies Defined by Symmetric Gates

Cited by 7 publications

References 11 publications

Parameterized exact and approximation algorithms for maximumk-set cover and related satisfiability problems

Parameterized exact and approximation algorithms for maximumk-set cover and related satisfiability problems

Parameterized algorithmics for computational social choice: Nine research challenges

How to Put through Your Agenda in Collective Binary Decisions

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