## Abstract

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: 2^{N} → 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 language | English |
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Title of host publication | Algorithms – ESA 2015 - 23rd Annual European Symposium, Proceedings |

Editors | Nikhil Bansal, Irene Finocchi |

Publisher | Springer Verlag |

Pages | 521-532 |

Number of pages | 12 |

ISBN (Print) | 9783662483497 |

DOIs | |

State | Published - 2015 |

Externally published | Yes |

Event | 23rd European Symposium on Algorithms, ESA 2015 - Patras, Greece Duration: 14 Sep 2015 → 16 Sep 2015 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 9294 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 23rd European Symposium on Algorithms, ESA 2015 |
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Country/Territory | Greece |

City | Patras |

Period | 14/09/15 → 16/09/15 |

### Bibliographical note

Publisher Copyright:© Springer-Verlag Berlin Heidelberg 2015.

## Keywords

- Cardinality constraint
- Matroid constraint
- Symmetric submodular functions