TY - GEN

T1 - Approximation algorithms for stochastic boolean function evaluation and stochastic submodular set cover

AU - Deshpande, Amol

AU - Hellerstein, Lisa

AU - Kletenik, Devorah

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

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U2 - 10.1137/1.9781611973402.107

DO - 10.1137/1.9781611973402.107

M3 - Conference contribution

AN - SCOPUS:84902106694

SN - 9781611973389

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 1453

EP - 1467

BT - Proceedings of the 25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014

PB - Association for Computing Machinery

T2 - 25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014

Y2 - 5 January 2014 through 7 January 2014

ER -