Deterministic algorithms for submodular maximization problems

Niv Buchbinder, Moran Feldman

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

Abstract

Randomization is a fundamental tool used in many theoretical and practical areas of computer science. We study here the role of randomization in the area of submodular function maximization. In this area most algorithms are randomized, and in almost all cases the approximation ratios obtained by current randomized algorithms are superior to the best results obtained by known deterministic algorithms. Derandomization of algorithms for general submodular function maximization seems hard since the access to the function is done via a value oracle. This makes it hard, for example, to apply standard derandomization techniques such as conditional expectations. Therefore, an interesting fundamental problem in this area is whether randomization is inherently necessary for obtaining good approximation ratios. In this work we give evidence that randomization is not necessary for obtaining good algorithms by presenting a new technique for derandomization of algorithms for submodular function maximization. Our high level idea is to maintain explicitly a (small) distribution over the states of the algorithm, and carefully update it using marginal values obtained from an extreme point solution of a suitable linear formulation. We demonstrate our technique on two recent algorithms for unconstrained submodular maximization and for maximizing submodular function subject to a cardinality constraint. In particular, for unconstrained submodular maximization we obtain an optimal deterministic 1/2-approximation showing that randomization is unnecessary for obtaining optimal results for this setting.

Original languageEnglish
Title of host publication27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016
EditorsRobert Krauthgamer
PublisherAssociation for Computing Machinery
Pages392-403
Number of pages12
ISBN (Electronic)9781510819672
DOIs
StatePublished - 2016
Event27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016 - Arlington, United States
Duration: 10 Jan 201612 Jan 2016

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
Volume1

Conference

Conference27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016
Country/TerritoryUnited States
CityArlington
Period10/01/1612/01/16

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