Maximizing symmetric submodular functions

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Symmetric submodular functions are an important family of submodular functions capturing many interesting cases including cut functions of graphs and hypergraphs. In this work, we identify submodular maximization problems for which one can get a better approximation for symmetric objectives compared to what is known for general submodular functions. For the problem of maximizing a non-negative symmetric submodular function f: 2 N → R+ subject to a down-monotone solvable polytope P ⊆ [0, 1] N, we describe an algorithm producing a fractional solution of value at least 0.432 · f(OPT), where OPT is the optimal integral solution. Our second result is a 0.432-approximation algorithm for the problem max{f(S): |S| = k} with a non-negative symmetric submodular function f: 2N → R+. Our method also applies to non-symmetric functions, in which case it produces 1/e − o(1) approximation. Finally, we describe a deterministic linear-time 1/2-approximation algorithm for unconstrained maximization of a non-negative symmetric submodular function.

Original languageAmerican English
Title of host publicationAlgorithms – ESA 2015 - 23rd Annual European Symposium, Proceedings
EditorsNikhil Bansal, Irene Finocchi
PublisherSpringer Verlag
Number of pages12
ISBN (Print)9783662483497
StatePublished - 2015
Externally publishedYes
Event23rd European Symposium on Algorithms, ESA 2015 - Patras, Greece
Duration: 14 Sep 201516 Sep 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)


Conference23rd European Symposium on Algorithms, ESA 2015


  • Cardinality constraint
  • Matroid constraint
  • Symmetric submodular functions

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science


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