A Parameterized Complexity Tutorial

Downey, Rodney G.

doi:10.1007/978-3-642-28332-1_4

Cited by 3 publications

(3 citation statements)

References 57 publications

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“…We assume the reader is familiar with the basic notions of (parameterized) complexity such as NP-hardness and fixedparameter tractability (FPT). For readers without these background, we refer to (Tovey 2002;Downey 2012). For an integer i, let…”

Section: Preliminariesmentioning

confidence: 99%

A Model of Winners Allocation

Yang

2021

AAAI

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We propose a model of winners allocation. In this model, we are given are two elections where the sets of candidates may intersect. The goal is to find two disjoint winning committees from respectively the two elections that are subjected to certain reasonable restrictions. For our model, we first propose several desirable properties. Then, we investigate the implication relationships among these properties. Finally, we study the complexity of computing winners allocations providing these properties. For hardness results, we also study some fixed-parameter algorithms.

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Section: Preliminariesmentioning

confidence: 99%

A Model of Winners Allocation

Yang

2021

AAAI

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“…We assume the reader is familiar with the basics in graph theory and (parameterized) complexity theory (Cygan et al, 2015;Downey, 2012;West, 2000;Tovey, 2002).…”

Section: Preliminariesmentioning

confidence: 99%

“…We assume the reader is familiar with the basics in graph theory and (parameterized) complexity [16,18,58,59].…”

Section: Preliminariesmentioning

confidence: 99%

Complexity of Manipulating and Controlling Approval-Based Multiwinner Voting

Yang

2019

Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence

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Tractable Triangles and Cross-Free Convexity in Discrete Optimisation

Cooper¹,

Živný²

2012

jair

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The minimisation problem of a sum of unary and pairwise functions of discrete variables is a general NP-hard problem with wide applications such as computing MAP configurations in Markov Random Fields (MRF), minimising Gibbs energy, or solving binary Valued Constraint Satisfaction Problems (VCSPs). We study the computational complexity of classes of discrete optimisation problems given by allowing only certain types of costs in every triangle of variable-value assignments to three distinct variables. We show that for several computational problems, the only non- trivial tractable classes are the well known maximum matching problem and the recently discovered joint-winner property. Our results, apart from giving complete classifications in the studied cases, provide guidance in the search for hybrid tractable classes; that is, classes of problems that are not captured by restrictions on the functions (such as submodularity) or the structure of the problem graph (such as bounded treewidth). Furthermore, we introduce a class of problems with convex cardinality functions on cross-free sets of assignments. We prove that while imposing only one of the two conditions renders the problem NP-hard, the conjunction of the two gives rise to a novel tractable class satisfying the cross-free convexity property, which generalises the joint-winner property to problems of unbounded arity.Comment: arXiv admin note: text overlap with arXiv:1008.4035 by other author

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A Parameterized Complexity Tutorial

Cited by 3 publications

References 57 publications

A Model of Winners Allocation

A Model of Winners Allocation

Complexity of Manipulating and Controlling Approval-Based Multiwinner Voting

Tractable Triangles and Cross-Free Convexity in Discrete Optimisation

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