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.ESA.2018.57
URN: urn:nbn:de:0030-drops-95208
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9520/
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Lee, Euiwoong ; Singla, Sahil

Optimal Online Contention Resolution Schemes via Ex-Ante Prophet Inequalities

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LIPIcs-ESA-2018-57.pdf (0.5 MB)

Abstract

Online contention resolution schemes (OCRSs) were proposed by Feldman, Svensson, and Zenklusen [Moran Feldman et al., 2016] as a generic technique to round a fractional solution in the matroid polytope in an online fashion. It has found applications in several stochastic combinatorial problems where there is a commitment constraint: on seeing the value of a stochastic element, the algorithm has to immediately and irrevocably decide whether to select it while always maintaining an independent set in the matroid. Although OCRSs immediately lead to prophet inequalities, these prophet inequalities are not optimal. Can we instead use prophet inequalities to design optimal OCRSs?
We design the first optimal 1/2-OCRS for matroids by reducing the problem to designing a matroid prophet inequality where we compare to the stronger benchmark of an ex-ante relaxation. We also introduce and design optimal (1-1/e)-random order CRSs for matroids, which are similar to OCRSs but the arrival order is chosen uniformly at random.

BibTeX - Entry

@InProceedings{lee_et_al:LIPIcs:2018:9520,
  author =	{Euiwoong Lee and Sahil Singla},
  title =	{{Optimal Online Contention Resolution Schemes via Ex-Ante Prophet Inequalities}},
  booktitle =	{26th Annual European Symposium on Algorithms (ESA 2018)},
  pages =	{57:1--57:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-081-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{112},
  editor =	{Yossi Azar and Hannah Bast and Grzegorz Herman},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9520},
  URN =		{urn:nbn:de:0030-drops-95208},
  doi =		{10.4230/LIPIcs.ESA.2018.57},
  annote =	{Keywords: Prophets, Contention Resolution, Stochastic Optimization, Matroids}
}

Keywords: Prophets, Contention Resolution, Stochastic Optimization, Matroids
Collection: 26th Annual European Symposium on Algorithms (ESA 2018)
Issue Date: 2018
Date of publication: 14.08.2018

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