### 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 |

Publisher | Springer Verlag |

Pages | 116-128 |

Number of pages | 13 |

Volume | 10138 LNCS |

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) | 03029743 |

ISSN (Electronic) | 16113349 |

### 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 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Approximation and Online Algorithms - 14th International Workshop, WAOA 2016, Revised Selected Papers*(Vol. 10138 LNCS, 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

**Scenario submodular cover.** / Grammel, Nathaniel; Hellerstein, Lisa; Kletenik, Devorah; Lin, Patrick.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Approximation and Online Algorithms - 14th International Workshop, WAOA 2016, Revised Selected Papers.*vol. 10138 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10138 LNCS, Springer Verlag, pp. 116-128, 14th International Workshop on Approximation and Online Algorithms, WAOA 2016, Aarhus, Denmark, 8/25/16. https://doi.org/10.1007/978-3-319-51741-4_10

}

TY - GEN

T1 - Scenario submodular cover

AU - Grammel, Nathaniel

AU - Hellerstein, Lisa

AU - Kletenik, Devorah

AU - Lin, Patrick

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85010695278&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85010695278&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-51741-4_10

DO - 10.1007/978-3-319-51741-4_10

M3 - Conference contribution

AN - SCOPUS:85010695278

SN - 9783319517407

VL - 10138 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 116

EP - 128

BT - Approximation and Online Algorithms - 14th International Workshop, WAOA 2016, Revised Selected Papers

PB - Springer Verlag

ER -