Comparing apples and oranges: Query tradeoff in submodular maximization

Niv Buchbinder, Moran Feldman, Roy Schwartz

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Fast algorithms for submodular maximization problems have a vast potential use in applicative settings, such as machine learning, social networks, and economics. Though fast algorithms were known for some special cases, only recently Badanidiyuru and Vondrak [4] were the first to explicitly look for such algorithms in the general case of maximizing a monotone submodular function subject to a matroid independence constraint. The algorithm of Badanidiyuru and Vondrak matches the best possible approximation guarantee, while trying to reduce the number of value oracle queries the algorithm performs. Our main result is a new algorithm for this general case which establishes a surprising tradeoff between two seemingly unrelated quantities: the number of value oracle queries and the number of matroid independence queries performed by the algorithm. Specifically, one can decrease the former by increasing the latter and vice versa, while maintaining the best possible approximation guarantee. Such a tradeoff is very useful since various applications might incur significantly different costs in querying the value and matroid independence oracles. Furthermore, in case the rank of the matroid is 0 (nc), where n is the size of the ground set and c is an absolute constant smaller than 1, the total number of oracle queries our algorithm uses can be made to have a smaller magnitude compared to that needed by [4j. We also provide even faster algorithms for the well studied special cases of a cardinality constraint and a partition matroid independence constraint, both of which capture many real-world applications and have been widely studied both theorically and in practice.

Original languageEnglish
Title of host publicationProceedings of the 26th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015
PublisherAssociation for Computing Machinery
Pages1149-1168
Number of pages20
EditionJanuary
ISBN (Electronic)9781611973747
DOIs
StatePublished - 2015
Externally publishedYes
Event26th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015 - San Diego, United States
Duration: 4 Jan 20156 Jan 2015

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
NumberJanuary
Volume2015-January

Conference

Conference26th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015
Country/TerritoryUnited States
CitySan Diego
Period4/01/156/01/15

ASJC Scopus subject areas

  • Software
  • Mathematics (all)

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