Streaming Submodular Maximization Under Matroid Constraints

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

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Author Details

Moran Feldman
  • University of Haifa, Israel
Paul Liu
  • Stanford University, CA, USA
Ashkan Norouzi-Fard
  • Google Research, Zurich, Switzerland
Ola Svensson
  • EPFL, Lausanne, Switzerland
Rico Zenklusen
  • ETH Zürich, Switzerland


The authors are very grateful to Jan Vondrák. It is safe to say that this paper would not be nearly as good without Jan’s many interesting discussions and comments.

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Moran Feldman, Paul Liu, Ashkan Norouzi-Fard, Ola Svensson, and Rico Zenklusen. Streaming Submodular Maximization Under Matroid Constraints. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 59:1-59:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Submodular optimization and polymatroids
  • Theory of computation → Streaming models
  • Submodular maximization
  • streaming
  • matroid
  • random order


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