Scenario submodular cover

Nathaniel Grammel, Lisa Hellerstein, Devorah Kletenik, Patrick Lin

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    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 languageEnglish (US)
    Title of host publicationApproximation and Online Algorithms - 14th International Workshop, WAOA 2016, Revised Selected Papers
    EditorsMonaldo Mastrolilli, Klaus Jansen
    PublisherSpringer Verlag
    Pages116-128
    Number of pages13
    ISBN (Print)9783319517407
    DOIs
    StatePublished - Jan 1 2017
    Event14th International Workshop on Approximation and Online Algorithms, WAOA 2016 - Aarhus, Denmark
    Duration: Aug 25 2016Aug 26 2016

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume10138 LNCS
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Other

    Other14th International Workshop on Approximation and Online Algorithms, WAOA 2016
    CountryDenmark
    CityAarhus
    Period8/25/168/26/16

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Computer Science(all)

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  • Cite this

    Grammel, N., Hellerstein, L., Kletenik, D., & Lin, P. (2017). Scenario submodular cover. In M. Mastrolilli, & K. Jansen (Eds.), 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