## Abstract

The weighted set cover problem is defined over a universe U of elements, and a set S of subsets of U, each of which is associated with a weight. The goal is then to find a subset C of S that collectively covers U, while having minimal weight. The decision version of this well-known problem is NP-complete, but approximation algorithms have been presented that are guaranteed to find a theta-approximation of the optimal solution, where theta is the harmonic sum of the size of the largest set in S. Finding minimal weight set covers is an important problem, used, e.g., in facility location, team formation and transaction summarization. This paper studies the enumeration version of this problem. Thus, we present an algorithm that enumerates all minimal weight set covers in polynomial delay (i.e., with polynomial time between results) in theta-approximate order. We also present a variant of this algorithm in order to enumerate non-redundant set covers in theta-approximate order. Experimental results show that our algorithms run well in practice over both real and synthetic data.

Original language | American English |
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Title of host publication | Proceedings - 2019 IEEE 35th International Conference on Data Engineering, ICDE 2019 |

Publisher | IEEE Computer Society |

Pages | 518-529 |

Number of pages | 12 |

ISBN (Electronic) | 9781538674741 |

DOIs | |

State | Published - Apr 2019 |

Event | 35th IEEE International Conference on Data Engineering, ICDE 2019 - Macau, China Duration: 8 Apr 2019 → 11 Apr 2019 |

### Publication series

Name | Proceedings - International Conference on Data Engineering |
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Volume | 2019-April |

ISSN (Print) | 1084-4627 |

### Conference

Conference | 35th IEEE International Conference on Data Engineering, ICDE 2019 |
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Country/Territory | China |

City | Macau |

Period | 8/04/19 → 11/04/19 |

### Bibliographical note

Funding Information:ACKNOWLEDGMENT The authors were partially supported by the Israel Science Foundation (Grant 879/16).

Publisher Copyright:

© 2019 IEEE.

## Keywords

- Approximation algorithm
- Enumeration
- Set cover