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

Jian Sun (), Haiyun Sheng, Yuefang Sun (), Donglei Du () and Xiaoyan Zhang ()
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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

Journal of Combinatorial Optimization, 2022, vol. 44, issue 4, No 25, 2626-2641

Abstract: 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.

Keywords: Stochastic optimization; Set cover; Rent or buy; Primal-dual; Approximation algorithms (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10878-021-00753-x

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