Unconstrained submodular maximization with constant adaptive complexity

Lin Chen, Moran Feldman, Amin Karbasi

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

Abstract

In this paper, we consider the unconstrained submodular maximization problem. We propose the first algorithm for this problem that achieves a tight (1/2 − ε)-approximation guarantee using Õ(ε−1) adaptive rounds and a linear number of function evaluations. No previously known algorithm for this problem achieves an approximation ratio better than 1/3 using less than Ω(n) rounds of adaptivity, where n is the size of the ground set. Moreover, our algorithm easily extends to the maximization of a non-negative continuous DR-submodular function subject to a box constraint, and achieves a tight (1/2 − ε)-approximation guarantee for this problem while keeping the same adaptive and query complexities.

Original languageEnglish
Title of host publicationSTOC 2019 - Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing
EditorsMoses Charikar, Edith Cohen
PublisherAssociation for Computing Machinery
Pages102-113
Number of pages12
ISBN (Electronic)9781450367059
DOIs
StatePublished - 23 Jun 2019
Externally publishedYes
Event51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019 - Phoenix, United States
Duration: 23 Jun 201926 Jun 2019

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017

Conference

Conference51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019
Country/TerritoryUnited States
CityPhoenix
Period23/06/1926/06/19

Bibliographical note

Publisher Copyright:
© 2019 Copyright held by the owner/author(s). Publication rights licensed to ACM.

Keywords

  • Low adaptive complexity
  • Parallel computation
  • Submodular maximization

ASJC Scopus subject areas

  • Software

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