License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2018.24
URN: urn:nbn:de:0030-drops-96069
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9606/
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Filos-Ratsikas, Aris ; Frederiksen, Søren Kristoffer Stiil ; Goldberg, Paul W. ; Zhang, Jie

Hardness Results for Consensus-Halving

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LIPIcs-MFCS-2018-24.pdf (0.6 MB)

Abstract

The Consensus-halving problem is the problem of dividing an object into two portions, such that each of n agents has equal valuation for the two portions. We study the epsilon-approximate version, which allows each agent to have an epsilon discrepancy on the values of the portions. It was recently proven in [Filos-Ratsikas and Goldberg, 2018] that the problem of computing an epsilon-approximate Consensus-halving solution (for n agents and n cuts) is PPA-complete when epsilon is inverse-exponential. In this paper, we prove that when epsilon is constant, the problem is PPAD-hard and the problem remains PPAD-hard when we allow a constant number of additional cuts. Additionally, we prove that deciding whether a solution with n-1 cuts exists for the problem is NP-hard.

BibTeX - Entry

@InProceedings{filosratsikas_et_al:LIPIcs:2018:9606,
  author =	{Aris Filos-Ratsikas and S\oren Kristoffer Stiil Frederiksen and Paul W. Goldberg and Jie Zhang},
  title =	{{Hardness Results for Consensus-Halving}},
  booktitle =	{43rd International Symposium on Mathematical Foundations  of Computer Science (MFCS 2018)},
  pages =	{24:1--24:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-086-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{117},
  editor =	{Igor Potapov and Paul Spirakis and James Worrell},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9606},
  URN =		{urn:nbn:de:0030-drops-96069},
  doi =		{10.4230/LIPIcs.MFCS.2018.24},
  annote =	{Keywords: PPAD, PPA, consensus halving, generalized-circuit, reduction}
}

Keywords: PPAD, PPA, consensus halving, generalized-circuit, reduction
Collection: 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)
Issue Date: 2018
Date of publication: 27.08.2018

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