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Maximizing Stochastic Monotone Submodular Functions

Author

Listed:
  • Arash Asadpour

    (Stern School of Business, New York University, New York, New York 10012)

  • Hamid Nazerzadeh

    (Marshall School of Business, University of Southern California, Los Angeles, California 90089)

Abstract

We study the problem of maximizing a stochastic monotone submodular function with respect to a matroid constraint. Because of the presence of diminishing marginal values in real-world problems, our model can capture the effect of stochasticity in a wide range of applications. We show that the adaptivity gap—the ratio between the values of optimal adaptive and optimal nonadaptive policies—is bounded and is equal to e /( e − 1). We propose a polynomial-time nonadaptive policy that achieves this bound. We also present an adaptive myopic policy that obtains at least half of the optimal value. Furthermore, when the matroid is uniform, the myopic policy achieves the optimal approximation ratio of 1 − 1/ e . This paper was accepted by Dimitris Bertsimas and Yinyu Ye, optimization .

Suggested Citation

  • Arash Asadpour & Hamid Nazerzadeh, 2016. "Maximizing Stochastic Monotone Submodular Functions," Management Science, INFORMS, vol. 62(8), pages 2374-2391, August.
    • Handle: RePEc:inm:ormnsc:v:62:y:2016:i:8:p:2374-2391
    DOI: 10.1287/mnsc.2015.2254
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    References listed on IDEAS

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    1. Fisher, M.L. & Nemhauser, G.L. & Wolsey, L.A., 1978. "An analysis of approximations for maximizing submodular set functions - 1," LIDAM Reprints CORE 334, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    5. Carri W. Chan & Vivek F. Farias, 2009. "Stochastic Depletion Problems: Effective Myopic Policies for a Class of Dynamic Optimization Problems," Mathematics of Operations Research, INFORMS, vol. 34(2), pages 333-350, May.
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    Cited by:

    1. Sekar, Shreyas & Vojnovic, Milan & Yun, Se-Young, 2020. "A test score based approach to stochastic submodular optimization," LSE Research Online Documents on Economics 103176, London School of Economics and Political Science, LSE Library.
    2. Yuhang Ma & Paat Rusmevichientong & Mika Sumida & Huseyin Topaloglu, 2020. "An Approximation Algorithm for Network Revenue Management Under Nonstationary Arrivals," Operations Research, INFORMS, vol. 68(3), pages 834-855, May.
    3. Shreyas Sekar & Milan Vojnovic & Se-Young Yun, 2021. "A Test Score-Based Approach to Stochastic Submodular Optimization," Management Science, INFORMS, vol. 67(2), pages 1075-1092, February.
    4. Shaojie Tang, 2022. "Robust Adaptive Submodular Maximization," INFORMS Journal on Computing, INFORMS, vol. 34(6), pages 3277-3291, November.

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