## Abstract

We consider the problem of maximizing the sum of a monotone submodular function and a linear function subject to a general solvable polytope constraint. Recently, Sviridenko et al. [16] described an algorithm for this problem whose approximation guarantee is optimal in some intuitive and formal senses. Unfortunately, this algorithm involves a guessing step which makes it less clean and significantly affects its time complexity. In this work we describe a clean alternative algorithm that uses a novel weighting technique in order to avoid the problematic guessing step while keeping the same approximation guarantee as the algorithm of [16].

Original language | English |
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Title of host publication | Algorithms and Data Structures - 16th International Symposium, WADS 2019, Proceedings |

Editors | Zachary Friggstad, Mohammad R. Salavatipour, Jörg-Rüdiger Sack |

Publisher | Springer Verlag |

Pages | 380-394 |

Number of pages | 15 |

ISBN (Print) | 9783030247652 |

DOIs | |

State | Published - 2019 |

Event | 16th International Symposium on Algorithms and Data Structures, WADS 2019 - Edmonton, Canada Duration: 5 Aug 2019 → 7 Aug 2019 |

### 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 | 11646 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 16th International Symposium on Algorithms and Data Structures, WADS 2019 |
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Country/Territory | Canada |

City | Edmonton |

Period | 5/08/19 → 7/08/19 |

### Bibliographical note

Funding Information:by Israel Science Foundation grant

Funding Information:

This research was partially supported by Israel Science Foundation grant number 1357/16.

Publisher Copyright:

© Springer Nature Switzerland AG 2019.

## Keywords

- Continuous greedy
- Curvature
- Submodular maximization