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.ICALP.2019.38
URN: urn:nbn:de:0030-drops-106143
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10614/
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Cheng, Siu-Wing ; Mao, Yuchen

Restricted Max-Min Allocation: Approximation and Integrality Gap

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LIPIcs-ICALP-2019-38.pdf (0.5 MB)

Abstract

Asadpour, Feige, and Saberi proved that the integrality gap of the configuration LP for the restricted max-min allocation problem is at most 4. However, their proof does not give a polynomial-time approximation algorithm. A lot of efforts have been devoted to designing an efficient algorithm whose approximation ratio can match this upper bound for the integrality gap. In ICALP 2018, we present a (6 + delta)-approximation algorithm where delta can be any positive constant, and there is still a gap of roughly 2. In this paper, we narrow the gap significantly by proposing a (4+delta)-approximation algorithm where delta can be any positive constant. The approximation ratio is with respect to the optimal value of the configuration LP, and the running time is poly(m,n)* n^{poly(1/(delta))} where n is the number of players and m is the number of resources. We also improve the upper bound for the integrality gap of the configuration LP to 3 + 21/26 =~ 3.808.

BibTeX - Entry

@InProceedings{cheng_et_al:LIPIcs:2019:10614,
  author =	{Siu-Wing Cheng and Yuchen Mao},
  title =	{{Restricted Max-Min Allocation: Approximation and Integrality Gap}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{38:1--38:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Christel Baier and Ioannis Chatzigiannakis and Paola Flocchini and Stefano Leonardi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10614},
  URN =		{urn:nbn:de:0030-drops-106143},
  doi =		{10.4230/LIPIcs.ICALP.2019.38},
  annote =	{Keywords: fair allocation, configuration LP, approximation, integrality gap}
}

Keywords: fair allocation, configuration LP, approximation, integrality gap
Collection: 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)
Issue Date: 2019
Date of publication: 04.07.2019

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