Approximation and Parameterized Complexity of Minimax Approval Voting

Marek Cygan, Łukasz Kowalik, Arkadiusz Socała, Krzysztof Sornat

Research output: Contribution to conferencePaperpeer-review

7 Scopus citations

Abstract

We present three results on the complexity of MINIMAX APPROVAL VOTING. First, we study MINIMAX APPROVAL VOTING parameterized by the Hamming distance d from the solution to the votes. We show MINIMAX APPROVAL VOTING admits no algorithm running in time O&z.ast; (2o(d log d)), unless the Exponential Time Hypothesis (ETH) fails. This means that the O&z.ast;(d2d) algorithm of Misra et al. [AAMAS 2015] is essentially optimal. Motivated by this, we then show a parameterized approximation scheme, running in time O&z.ast;((3/e)2), which is essentially tight assuming ETH. Finally, we get a new polynomial-time randomized approximation scheme for MINIMAX APPROVAL VOTING, which runs intimenO(1/e2·log(1/ϵ)) · poly (m), almost matching the running time of the fastest known PTAS for CLOSEST STRING due to Ma and Sun [SIAM J. Comp. 2009].

Original languageEnglish
Pages459-465
Number of pages7
StatePublished - 2017
Externally publishedYes
Event31st AAAI Conference on Artificial Intelligence, AAAI 2017 - San Francisco, United States
Duration: 4 Feb 201710 Feb 2017

Conference

Conference31st AAAI Conference on Artificial Intelligence, AAAI 2017
Country/TerritoryUnited States
CitySan Francisco
Period4/02/1710/02/17

ASJC Scopus subject areas

  • Artificial Intelligence

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