### Abstract

We present approximation algorithms for two problems: Stochastic Boolean Function Evaluation (SBFE) and Stochastic Submodular Set Cover (SSSC). Our results for SBFE problems are obtained by reducing them to SSSC problems through the construction of appropriate utility functions. We give a new algorithm for the SSSC problem that we call Adaptive Dual Greedy. We use this algorithm to obtain a 3-approximation algorithm solving the SBFE problem for linear threshold formulas. We also get a 3-approximation algorithm for the closely related Stochastic Min-Knapsack problem, and a 2-approximation for a natural special case of that problem. In addition, we prove a new approximation bound for a previous algorithm for the SSSC problem, Adaptive Greedy. We consider an approach to approximating SBFE problems using existing techniques, which we call the Q-value approach. This approach easily yields a new result for evaluation of CDNF formulas, and we apply variants of it to simultaneous evaluation problems and a ranking problem. However, we show that the Q-value approach provably cannot be used to obtain a sublinear approximation factor for the SBFE problem for linear threshold formulas or read-once DNF.

Original language | English (US) |
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Title of host publication | Proceedings of the 25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014 |

Publisher | Association for Computing Machinery |

Pages | 1453-1467 |

Number of pages | 15 |

ISBN (Print) | 9781611973389 |

DOIs | |

State | Published - 2014 |

Event | 25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014 - Portland, OR, United States Duration: Jan 5 2014 → Jan 7 2014 |

### Publication series

Name | Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms |
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### Other

Other | 25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014 |
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Country | United States |

City | Portland, OR |

Period | 1/5/14 → 1/7/14 |

### ASJC Scopus subject areas

- Software
- Mathematics(all)

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## Cite this

*Proceedings of the 25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014*(pp. 1453-1467). (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms). Association for Computing Machinery. https://doi.org/10.1137/1.9781611973402.107