Hitting and Covering Partially

Agrawal, Akanksha; Choudhary, Pratibha; Jain, Pallavi; Kanesh, Lawqueen; Sahlot, Vibha; Saurabh, Saket

doi:10.1007/978-3-319-94776-1_62

Cited by 3 publications

(15 citation statements)

References 21 publications

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“…Concretely, we obtain FPT results for WD-MAV and WD-CCAV with respect to both the combined parameter k + C and the combined parameter k + C . However, we show that WD-MAV and WD-CCAV are W [1]-hard with respect to the combined parameter k + V . With respect to the combined parameter k + V , we develop an FPT-algorithm for WD-MAV but show that WD-CCAV is W[1]-hard.…”

Section: Combined Parametersmentioning

confidence: 68%

“…To the best of our knowledge, this parameter has not been studied for these rules so far. With respect to this parameter, we show that WD-MAV, WD-CCAV, and WD-PAV are W [1]-hard. Third, based on previous results we achieve some dichotomy results with respect to the two natural parameters C and V .…”

Section: Single Parametersmentioning

confidence: 97%

“…CCAV selects k-committees with the maximum CCAV score 1 . PAV The satisfaction degree of a vote v obtained from a committee w is…”

Section: Preliminariesmentioning

confidence: 99%

“…It is easy to see that WINNER DETERMINATION for PAV, MAV, and CCAV is FPT with respect to the parameter m. Misra, Nabeel, and Singh [46] proved that WD-MAV is FPT with respect to the parameters d and n, but becomes W [2]-hard with respect to the parameter k. Betzler, Slinko, and Uhlmann [4] proved that WD-CCAV is FPT with respect to the parameter n, but turned out to be W [2]-hard with respect to the parameter k. Moreover, they considered a dual parameter R = n − d. They proved that WD-CCAV is NP-hard even for R = 0, but presented an FPT-algorithm with respect to the combined parameter k + R. Aziz et al [3] proved that WD-PAV is W [1]-hard with respect to k even if every voter approves at most two candidates.…”

Section: Single Parametersmentioning

confidence: 99%

“…A parameterized problem can be either fixed-parameter tractable (FPT) or fixed-parameter intractable. In particular, a parameterized problem is FPT if there is an algorithm which correctly determines whether every given instance (I, κ) is a Yes-instance in O( f (k) • |I| O (1) )-time, where f (k) is a computable function in k. Fixed-parameter intractable problems are further classified into many classes including W [1]-hard, W [2]-hard, etc. Parameterized complexity was pioneered by Downey and Fellows [21,23], and has been successfully used to dealing with many NP-hard problems.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Parameterized Complexity of Multi-winner Determination: More Effort Towards Fixed-Parameter Tractability

Yang¹,

Wang²

2021

Preprint

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We study winner determination for three prevalent k-committee selection rules, namely minimax approval voting (MAV), proportional approval voting (PAV), and Chamberlin-Courant's approval voting (CCAV). It is known that winner determination for these rules is NP-hard. Parameterized complexity of the problem has been studied with respect to some natural parameters recently. However, there are still numerous parameters that have not been considered. We revisit the parameterized complexity of winner determination by considering several important single parameters, combined parameters, and structural parameters, aiming at detecting more interesting parameters leading to fixed-parameter tractability results.

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Section: Combined Parametersmentioning

confidence: 68%

Section: Single Parametersmentioning

confidence: 97%

“…CCAV selects k-committees with the maximum CCAV score 1 . PAV The satisfaction degree of a vote v obtained from a committee w is…”

Section: Preliminariesmentioning

confidence: 99%

Section: Single Parametersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Parameterized Complexity of Multi-winner Determination: More Effort Towards Fixed-Parameter Tractability

Yang¹,

Wang²

2021

Preprint

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Max-SAT with Cardinality Constraint Parameterized by the Number of Clauses

Jain,

Kanesh,

Panolan

et al. 2024

Lecture Notes in Computer Science

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Parameterized complexity of multiwinner determination: more effort towards fixed-parameter tractability

Yang

Wang

2023

Auton Agent Multi-Agent Syst

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We study the parameterized complexity of winner determination problems for three prevalent k-committee selection rules, namely the minimax approval voting (MAV), the proportional approval voting (PAV), and the Chamberlin–Courant’s approval voting (CCAV). It is known that these problems are computationally hard. Although they have been studied from the parameterized complexity point of view with respect to several natural parameters, many of them turned out to be -hard or -hard. Aiming at obtaining plentiful fixed-parameter algorithms, we revisit these problems by considering more natural single parameters, combined parameters, and structural parameters.

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Hitting and Covering Partially

Cited by 3 publications

References 21 publications

Parameterized Complexity of Multi-winner Determination: More Effort Towards Fixed-Parameter Tractability

Parameterized Complexity of Multi-winner Determination: More Effort Towards Fixed-Parameter Tractability

Max-SAT with Cardinality Constraint Parameterized by the Number of Clauses

Parameterized complexity of multiwinner determination: more effort towards fixed-parameter tractability

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