License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2020.62
URN: urn:nbn:de:0030-drops-126657
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12665/
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Huang, Chien-Chung ; Thiery, Theophile ; Ward, Justin

Improved Multi-Pass Streaming Algorithms for Submodular Maximization with Matroid Constraints

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LIPIcs-APPROX62.pdf (0.6 MB)

Abstract

We give improved multi-pass streaming algorithms for the problem of maximizing a monotone or arbitrary non-negative submodular function subject to a general p-matchoid constraint in the model in which elements of the ground set arrive one at a time in a stream. The family of constraints we consider generalizes both the intersection of p arbitrary matroid constraints and p-uniform hypergraph matching. For monotone submodular functions, our algorithm attains a guarantee of p+1+ε using O(p/ε)-passes and requires storing only O(k) elements, where k is the maximum size of feasible solution. This immediately gives an O(1/ε)-pass (2+ε)-approximation for monotone submodular maximization in a matroid and (3+ε)-approximation for monotone submodular matching. Our algorithm is oblivious to the choice ε and can be stopped after any number of passes, delivering the appropriate guarantee. We extend our techniques to obtain the first multi-pass streaming algorithms for general, non-negative submodular functions subject to a p-matchoid constraint. We show that a randomized O(p/ε)-pass algorithm storing O(p³klog(k)/ε³) elements gives a (p+1+γ+O(ε))-approximation, where γ is the guarantee of the best-known offline algorithm for the same problem.

BibTeX - Entry

@InProceedings{huang_et_al:LIPIcs:2020:12665,
  author =	{Chien-Chung Huang and Theophile Thiery and Justin Ward},
  title =	{{Improved Multi-Pass Streaming Algorithms for Submodular Maximization with Matroid Constraints}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)},
  pages =	{62:1--62:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-164-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{176},
  editor =	{Jaros{\l}aw Byrka and Raghu Meka},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12665},
  URN =		{urn:nbn:de:0030-drops-126657},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2020.62},
  annote =	{Keywords: submodular maximization, streaming algorithms, matroid, matchoid}
}

Keywords: submodular maximization, streaming algorithms, matroid, matchoid
Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)
Issue Date: 2020
Date of publication: 11.08.2020

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