Optimal online contention resolution schemes via ex-ante prophet inequalities

Euiwoong Lee, Sahil Singla

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

Online contention resolution schemes (OCRSs) were proposed by Feldman, Svensson, and Zenklusen [11] 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.

Original languageEnglish (US)
Title of host publication26th European Symposium on Algorithms, ESA 2018
EditorsHannah Bast, Grzegorz Herman, Yossi Azar
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Print)9783959770811
DOIs
StatePublished - Aug 1 2018
Externally publishedYes
Event26th European Symposium on Algorithms, ESA 2018 - Helsinki, Finland
Duration: Aug 20 2018Aug 22 2018

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume112
ISSN (Print)1868-8969

Other

Other26th European Symposium on Algorithms, ESA 2018
CountryFinland
CityHelsinki
Period8/20/188/22/18

All Science Journal Classification (ASJC) codes

  • Software

Keywords

  • Contention resolution
  • Matroids
  • Prophets
  • Stochastic optimization

Cite this

Lee, E., & Singla, S. (2018). Optimal online contention resolution schemes via ex-ante prophet inequalities. In H. Bast, G. Herman, & Y. Azar (Eds.), 26th European Symposium on Algorithms, ESA 2018 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 112). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.ESA.2018.57