### Abstract

We introduce the Scenario Submodular Cover problem. In this problem, the goal is to produce a cover with minimum expected cost, with respect to an empirical joint probability distribution, given as input by a weighted sample of realizations. The problem is a counterpart to the Stochastic Submodular Cover problem studied by Golovin and Krause [6], which assumes independent variables. We give two approximation algorithms for Scenario Submodular Cover. Assuming an integervalued utility function and integer weights, the first achieves an approximation factor of O(logQm), where m is the sample size and Q is the goal utility. The second, simpler algorithm achieves an approximation factor of O(logQW), where W is the sum of the weights. We achieve our bounds by building on previous related work (in [4,6,15]) and by exploiting a technique we call the Scenario-OR modification. We apply these algorithms to a new problem, Scenario Boolean Function Evaluation. Our results have applciations to other problems involving distributions that are explicitly specified by their support.

Original language | English (US) |
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Title of host publication | Approximation and Online Algorithms - 14th International Workshop, WAOA 2016, Revised Selected Papers |

Editors | Monaldo Mastrolilli, Klaus Jansen |

Publisher | Springer Verlag |

Pages | 116-128 |

Number of pages | 13 |

ISBN (Print) | 9783319517407 |

DOIs | |

State | Published - 2017 |

Event | 14th International Workshop on Approximation and Online Algorithms, WAOA 2016 - Aarhus, Denmark Duration: Aug 25 2016 → Aug 26 2016 |

### 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 | 10138 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 14th International Workshop on Approximation and Online Algorithms, WAOA 2016 |
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Country | Denmark |

City | Aarhus |

Period | 8/25/16 → 8/26/16 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Approximation and Online Algorithms - 14th International Workshop, WAOA 2016, Revised Selected Papers*(pp. 116-128). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10138 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-51741-4_10