TY - GEN

T1 - Scenario submodular cover

AU - Grammel, Nathaniel

AU - Hellerstein, Lisa

AU - Kletenik, Devorah

AU - Lin, Patrick

N1 - Publisher Copyright:
© Springer International Publishing AG 2017.

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.

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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

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

A2 - Mastrolilli, Monaldo

A2 - Jansen, Klaus

PB - Springer Verlag

T2 - 14th International Workshop on Approximation and Online Algorithms, WAOA 2016

Y2 - 25 August 2016 through 26 August 2016

ER -