## Abstract

In this paper, we consider the unconstrained submodular maximization problem. We propose the first algorithm for this problem that achieves a tight (1/2 − ε)-approximation guarantee using Õ(ε^{−1}) adaptive rounds and a linear number of function evaluations. No previously known algorithm for this problem achieves an approximation ratio better than 1/3 using less than Ω(n) rounds of adaptivity, where n is the size of the ground set. Moreover, our algorithm easily extends to the maximization of a non-negative continuous DR-submodular function subject to a box constraint, and achieves a tight (1/2 − ε)-approximation guarantee for this problem while keeping the same adaptive and query complexities.

Original language | English |
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Title of host publication | STOC 2019 - Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing |

Editors | Moses Charikar, Edith Cohen |

Publisher | Association for Computing Machinery |

Pages | 102-113 |

Number of pages | 12 |

ISBN (Electronic) | 9781450367059 |

DOIs | |

State | Published - 23 Jun 2019 |

Event | 51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019 - Phoenix, United States Duration: 23 Jun 2019 → 26 Jun 2019 |

### Publication series

Name | Proceedings of the Annual ACM Symposium on Theory of Computing |
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ISSN (Print) | 0737-8017 |

### Conference

Conference | 51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019 |
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Country/Territory | United States |

City | Phoenix |

Period | 23/06/19 → 26/06/19 |

### Bibliographical note

Funding Information:Lin Chen was supported by Google PhD Fellowship, Moran Feldman was supported in part by ISF grant 1357/16, and Amin Karbasi was supported by AFOSR YIP award (FA9550-18-1-0160).

## Keywords

- Low adaptive complexity
- Parallel computation
- Submodular maximization