The one-way communication complexity of submodular maximization with applications to streaming and robustness

Moran Feldman, Ashkan Norouzi-Fard, Ola Svensson, Rico Zenklusen

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

Abstract

We consider the classical problem of maximizing a monotone submodular function subject to a cardinality constraint, which, due to its numerous applications, has recently been studied in various computational models. We consider a clean multi-player model that lies between the offline and streaming model, and study it under the aspect of one-way communication complexity. Our model captures the streaming setting (by considering a large number of players), and, in addition, two player approximation results for it translate into the robust setting. We present tight one-way communication complexity results for our model, which, due to the above-mentioned connections, have multiple implications in the data stream and robust setting. Even for just two players, a prior information-theoretic hardness result implies that no approximation factor above 1/2 can be achieved in our model, if only queries to feasible sets, i.e., sets respecting the cardinality constraint, are allowed. We show that the possibility of querying infeasible sets can actually be exploited to beat this bound, by presenting a tight 2/3-approximation taking exponential time, and an efficient 0.514-approximation. To the best of our knowledge, this is the first example where querying a submodular function on infeasible sets leads to provably better results. Through the above-mentioned link to the robust setting, both of these algorithms improve on the current state-of-the-art for robust submodular maximization, showing that approximation factors beyond 1/2 are possible. Moreover, exploiting the link of our model to streaming, we settle the approximability for streaming algorithms by presenting a tight 1/2+ϵ hardness result, based on the construction of a new family of coverage functions. This improves on a prior 1-1/e+ϵ hardness and matches, up to an arbitrarily small margin, the best known approximation algorithm.

Original languageEnglish
Title of host publicationSTOC 2020 - Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing
EditorsKonstantin Makarychev, Yury Makarychev, Madhur Tulsiani, Gautam Kamath, Julia Chuzhoy
PublisherAssociation for Computing Machinery
Pages1363-1374
Number of pages12
ISBN (Electronic)9781450369794
DOIs
StatePublished - 8 Jun 2020
Event52nd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2020 - Chicago, United States
Duration: 22 Jun 202026 Jun 2020

Publication series

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

Conference

Conference52nd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2020
Country/TerritoryUnited States
CityChicago
Period22/06/2026/06/20

Bibliographical note

Funding Information:
The first author was supported in part by the Israel Science Foundation (ISF) under grant no. 1357/16. The third author was supported by the Swiss National Science Foundation under grant no. 200021-184656 “Randomness in Problem Instances and Randomized Algorithms.” The last author was supported by Swiss National Science Foundation grants 200021_184622 and 200021_165866, and by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 817750).

Publisher Copyright:
© 2020 ACM.

Keywords

  • Approximation Algorithms
  • Communication Complexity
  • Robustness
  • Streaming
  • Submodular Maximization

ASJC Scopus subject areas

  • Software

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