Combinatorial prophet inequalities

Aviad Rubinstein, Sahil Singla

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

27 Scopus citations

Abstract

We introduce a novel framework of Prophet Inequalities for combinatorial valuation functions. For a (non-monotone) submodular objective function over an arbitrary matroid feasibility constraint, we give an O(1)-competitive algorithm. For a monotone subadditive objective function over an arbitrary downwardclosed feasibility constraint, we give an O(log n log2 r) competitive algorithm (where r is the cardinality of the largest feasible subset). Inspired by the proof of our subadditive prophet inequality, we also obtain an O(log n log2 r)-competitive algorithm for the Secretary Problem with a monotone subadditive objective function subject to an arbitrary downward-closed feasibility constraint. Even for the special case of a cardinality feasibility constraint, our algorithm circumvents an ( p n) lower bound by Bateni, Hajiaghayi, and Zadimoghaddam [10] in a restricted query model. En route to our submodular prophet inequality, we prove a technical result of independent interest: we show a variant of the Correlation Gap Lemma [14, 1] for nonmonotone submodular functions.

Original languageEnglish (US)
Title of host publication28th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017
EditorsPhilip N. Klein
PublisherAssociation for Computing Machinery
Pages1671-1687
Number of pages17
ISBN (Electronic)9781611974782
StatePublished - Jan 1 2017
Externally publishedYes
Event28th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017 - Barcelona, Spain
Duration: Jan 16 2017Jan 19 2017

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Other

Other28th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017
CountrySpain
CityBarcelona
Period1/16/171/19/17

All Science Journal Classification (ASJC) codes

  • Software
  • Mathematics(all)

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