Constrained Submodular Maximization via New Bounds for DR-Submodular Functions

Niv Buchbinder, Moran Feldman

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

Abstract

Submodular maximization under various constraints is a fundamental problem studied continuously, in both computer science and operations research, since the late 1970's. A central technique in this field is to approximately optimize the multilinear extension of the submodular objective, and then round the solution. The use of this technique requires a solver able to approximately maximize multilinear extensions. Following a long line of work, Buchbinder and Feldman (2019) described such a solver guaranteeing 0.385-approximation for down-closed constraints, while Oveis Gharan and Vondrák (2011) showed that no solver can guarantee better than 0.478-approximation. In this paper, we present a solver guaranteeing 0.401-approximation, which significantly reduces the gap between the best known solver and the inapproximability result. The design and analysis of our solver are based on a novel bound that we prove for DR-submodular functions. This bound improves over a previous bound due to Feldman et al. (2011) that is used by essentially all state-of-the-art results for constrained maximization of general submodular/DR-submodular functions. Hence, we believe that our new bound is likely to find many additional applications in related problems, and to be a key component for further improvement.

Original languageEnglish
Title of host publicationSTOC 2024 - Proceedings of the 56th Annual ACM Symposium on Theory of Computing
EditorsBojan Mohar, Igor Shinkar, Ryan O�Donnell
PublisherAssociation for Computing Machinery
Pages1820-1831
Number of pages12
ISBN (Electronic)9798400703836
DOIs
StatePublished - 10 Jun 2024
Externally publishedYes
Event56th Annual ACM Symposium on Theory of Computing, STOC 2024 - Vancouver, Canada
Duration: 24 Jun 202428 Jun 2024

Publication series

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

Conference

Conference56th Annual ACM Symposium on Theory of Computing, STOC 2024
Country/TerritoryCanada
CityVancouver
Period24/06/2428/06/24

Bibliographical note

Publisher Copyright:
© 2024 Copyright is held by the owner/author(s). Publication rights licensed to ACM.

Keywords

  • convex-body constraint
  • DR-submodular functions
  • knapsack constraints
  • matroid constraint
  • submodular functions

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