Tournament Fixing Parameterized by Feedback Vertex Set Number Is FPT

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3 Scopus citations

Abstract

A knockout (or single-elimination) tournament is a format of a competition that is very popular in practice (particularly in sports, elections and decision making), and which has been extensively and intensively studied from a theoretical point of view for more than a decade. Particular attention has been devoted to the TOURNAMENT FIXING problem, where, roughly speaking, the objective is to determine whether we can conduct the knockout tournament in a way that makes our favorite player win. Here, part of the input is a tournament graph D that encodes the winner of each possible match. A sequence of papers has studied the parameterized complexity of TOURNAMENT FIXING with respect to the feedback arc set number (fas) of D. Given that this parameter yielded tractability, it has been asked explicitly and repeatedly whether TOURNAMENT FIXING is FPT also with respect to the feedback vertex set number (fvs) of D. We answer this question positively. In fact, although fvs can be arbitrarily smaller than fas, we attain the same dependency on the parameter in the time complexity. So, additionally, our work subsumes the best known algorithm for TOURNAMENT FIXING with respect to fas.

Original languageEnglish
Title of host publicationAAAI-23 Technical Tracks 5
EditorsBrian Williams, Yiling Chen, Jennifer Neville
PublisherAAAI press
Pages5876-5883
Number of pages8
ISBN (Electronic)9781577358800
StatePublished - 27 Jun 2023
Event37th AAAI Conference on Artificial Intelligence, AAAI 2023 - Washington, United States
Duration: 7 Feb 202314 Feb 2023

Publication series

NameProceedings of the 37th AAAI Conference on Artificial Intelligence, AAAI 2023
Volume37

Conference

Conference37th AAAI Conference on Artificial Intelligence, AAAI 2023
Country/TerritoryUnited States
CityWashington
Period7/02/2314/02/23

ASJC Scopus subject areas

  • Artificial Intelligence

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