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Approximation algorithms for stochastic set cover and single sink rent-or-buy with submodular penalty

Author

Listed:
  • Jian Sun

    (Beijing University of Technology)

  • Haiyun Sheng

    (Nanjing Normal University)

  • Yuefang Sun

    (Ningbo University)

  • Donglei Du

    (University of New Brunswick)

  • Xiaoyan Zhang

    (Nanjing Normal University)

Abstract

Stochastic combinatorial optimization problems are usually defined as planning problems, which involve purchasing and allocating resources in order to meet uncertain needs. For example, network designers need to make their best guess about the future needs of the network and purchase capabilities accordingly. Facing uncertain in the future, we either “wait and see” changes, or postpone decisions about resource allocation until the requirements or constraints become realized. Specifically, in the field of stochastic combinatorial optimization, some inputs of the problems are uncertain, but follow known probability distributions. Our goal is to find a strategy that minimizes the expected cost. In this paper, we consider the two-stage finite-scenario stochastic set cover problem and the single sink rent-or-buy problem by presenting primal-dual based approximation algorithms for these two problems with approximation ratio $$2\eta $$ 2 η and 4.39, respectively, where $$\eta $$ η is the maximum frequency of the element of the ground set in the set cover problem.

Suggested Citation

  • Jian Sun & Haiyun Sheng & Yuefang Sun & Donglei Du & Xiaoyan Zhang, 2022. "Approximation algorithms for stochastic set cover and single sink rent-or-buy with submodular penalty," Journal of Combinatorial Optimization, Springer, vol. 44(4), pages 2626-2641, November.
    • Handle: RePEc:spr:jcomop:v:44:y:2022:i:4:d:10.1007_s10878-021-00753-x
    DOI: 10.1007/s10878-021-00753-x
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    References listed on IDEAS

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    1. Youngho Lee & Steve Y. Chiu & Jennifer Ryan, 1996. "A Branch and Cut Algorithm for a Steiner Tree-Star Problem," INFORMS Journal on Computing, INFORMS, vol. 8(3), pages 194-201, August.
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