Maximizing Sums of Non-Monotone Submodular and Linear Functions: Understanding the Unconstrained Case

Kobi Bodek, Moran Feldman

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

Abstract

Motivated by practical applications, recent works have considered maximization of sums of a submodular function g and a linear function ℓ. Almost all such works, to date, studied only the special case of this problem in which g is also guaranteed to be monotone. Therefore, in this paper we systematically study the simplest version of this problem in which g is allowed to be non-monotone, namely the unconstrained variant, which we term Regularized Unconstrained Submodular Maximization (RegularizedUSM). Our main algorithmic result is the first non-trivial guarantee for general RegularizedUSM. For the special case of RegularizedUSM in which the linear function ℓ is non-positive, we prove two inapproximability results, showing that the algorithmic result implied for this case by previous works is not far from optimal. Finally, we reanalyze the known Double Greedy algorithm to obtain improved guarantees for the special case of RegularizedUSM in which the linear function ℓ is non-negative; and we complement these guarantees by showing that it is not possible to obtain (1/2, 1)-approximation for this case (despite intuitive arguments suggesting that this approximation guarantee is natural).

Original languageEnglish
Title of host publication30th Annual European Symposium on Algorithms, ESA 2022
EditorsShiri Chechik, Gonzalo Navarro, Eva Rotenberg, Grzegorz Herman
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages23:1-23:17
Number of pages17
ISBN (Electronic)9783959772471
DOIs
StatePublished - 1 Sep 2022
Externally publishedYes
Event30th Annual European Symposium on Algorithms, ESA 2022 - Berlin/Potsdam, Germany
Duration: 5 Sep 20229 Sep 2022

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume244
ISSN (Print)1868-8969

Conference

Conference30th Annual European Symposium on Algorithms, ESA 2022
Country/TerritoryGermany
CityBerlin/Potsdam
Period5/09/229/09/22

Bibliographical note

Publisher Copyright:
© 2022 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. All rights reserved.

Keywords

  • Unconstrained submodular maximization
  • double greedy
  • inapproximability
  • non-oblivious local search
  • regularization

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