Maximizing Non-Monotone Submodular Functions over Small Subsets: Beyond 1/2-Approximation

Authors Aviad Rubinstein, Junyao Zhao

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Aviad Rubinstein
  • Computer Science Department, Stanford University, CA, USA
Junyao Zhao
  • Computer Science Department, Stanford University, CA, USA

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Aviad Rubinstein and Junyao Zhao. Maximizing Non-Monotone Submodular Functions over Small Subsets: Beyond 1/2-Approximation. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 106:1-106:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


In this work we give two new algorithms that use similar techniques for (non-monotone) submodular function maximization subject to a cardinality constraint. The first is an offline fixed-parameter tractable algorithm that guarantees a 0.539-approximation for all non-negative submodular functions. The second algorithm works in the random-order streaming model. It guarantees a (1/2+c)-approximation for symmetric functions, and we complement it by showing that no space-efficient algorithm can beat 1/2 for asymmetric functions. To the best of our knowledge this is the first provable separation between symmetric and asymmetric submodular function maximization.

Subject Classification

ACM Subject Classification
  • Theory of computation → Submodular optimization and polymatroids
  • Submodular optimization
  • Fixed-parameter tractability
  • Random-order streaming


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