License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2022.45
URN: urn:nbn:de:0030-drops-158555
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/15855/
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Lampis, Michael

Determining a Slater Winner Is Complete for Parallel Access to NP

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LIPIcs-STACS-2022-45.pdf (0.7 MB)

Abstract

We consider the complexity of deciding the winner of an election under the Slater rule. In this setting we are given a tournament T = (V,A), where the vertices of V represent candidates and the direction of each arc indicates which of the two endpoints is preferable for the majority of voters. The Slater score of a vertex v ∈ V is defined as the minimum number of arcs that need to be reversed so that T becomes acyclic and v becomes the winner. We say that v is a Slater winner in T if v has minimum Slater score in T.
Deciding if a vertex is a Slater winner in a tournament has long been known to be NP-hard. However, the best known complexity upper bound for this problem is the class Θ₂^p, which corresponds to polynomial-time Turing machines with parallel access to an NP oracle. In this paper we close this gap by showing that the problem is Θ₂^p-complete, and that this hardness applies to instances constructible by aggregating the preferences of 7 voters.

BibTeX - Entry

@InProceedings{lampis:LIPIcs.STACS.2022.45,
  author =	{Lampis, Michael},
  title =	{{Determining a Slater Winner Is Complete for Parallel Access to NP}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{45:1--45:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/15855},
  URN =		{urn:nbn:de:0030-drops-158555},
  doi =		{10.4230/LIPIcs.STACS.2022.45},
  annote =	{Keywords: Slater winner, Feedback Arc Set, Tournaments}
}

Keywords: Slater winner, Feedback Arc Set, Tournaments
Collection: 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)
Issue Date: 2022
Date of publication: 09.03.2022

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