Streaming Submodular Maximization Under Matroid Constraints

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

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

Abstract

Recent progress in (semi-)streaming algorithms for monotone submodular function maximization has led to tight results for a simple cardinality constraint. However, current techniques fail to give a similar understanding for natural generalizations, including matroid constraints. This paper aims at closing this gap. For a single matroid of rank k (i.e., any solution has cardinality at most k), our main results are: A single-pass streaming algorithm that uses Õ(k) memory and achieves an approximation guarantee of 0.3178. A multi-pass streaming algorithm that uses Õ(k) memory and achieves an approximation guarantee of (1 − 1/e − ε) by taking a constant (depending on ε) number of passes over the stream. This improves on the previously best approximation guarantees of 1/4 and 1/2 for single-pass and multi-pass streaming algorithms, respectively. In fact, our multi-pass streaming algorithm is tight in that any algorithm with a better guarantee than 1/2 must make several passes through the stream and any algorithm that beats our guarantee of 1 − 1/e must make linearly many passes (as well as an exponential number of value oracle queries). Moreover, we show how the approach we use for multi-pass streaming can be further strengthened if the elements of the stream arrive in uniformly random order, implying an improved result for p-matchoid constraints.

Original languageEnglish
Title of host publication49th EATCS International Conference on Automata, Languages, and Programming, ICALP 2022
EditorsMikolaj Bojanczyk, Emanuela Merelli, David P. Woodruff
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959772358
DOIs
StatePublished - 1 Jul 2022
Event49th EATCS International Conference on Automata, Languages, and Programming, ICALP 2022 - Paris, France
Duration: 4 Jul 20228 Jul 2022

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume229
ISSN (Print)1868-8969

Conference

Conference49th EATCS International Conference on Automata, Languages, and Programming, ICALP 2022
Country/TerritoryFrance
CityParis
Period4/07/228/07/22

Bibliographical note

Funding Information:
Funding Moran Feldman: Research supported in part by the Israel Science Foundation (ISF) grants no. 1357/16 and 459/20. Ola Svensson: Research supported by the Swiss National Science Foundation project 200021-184656 “Randomness in Problem Instances and Randomized Algorithms.” Rico Zenklusen: Research supported in part by Swiss National Science Foundation grant number 200021_184622. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 817750).

Funding Information:
Moran Feldman: Research supported in part by the Israel Science Foundation (ISF) grants no. 1357/16 and 459/20. Ola Svensson: Research supported by the Swiss National Science Foundation project 200021-184656 “Randomness in Problem Instances and Randomized Algorithms.” Rico Zenklusen: Research supported in part by Swiss National Science Foundation grant number 200021_184622. This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 817750).

Publisher Copyright:
© Moran Feldman, Paul Liu, Ashkan Norouzi-Fard, Ola Svensson, and Rico Zenklusen; licensed under Creative Commons License CC-BY 4.0

Keywords

  • matroid
  • random order
  • streaming
  • Submodular maximization

ASJC Scopus subject areas

  • Software

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