A combinatorial approximation algorithm for k-level facility location problem with submodular penalties

Li Zhang, Jing Yuan, Zhizhen Xu and Qiaoliang Li ()
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Li Zhang: Hunan Normal University
Jing Yuan: Hunan Normal University
Zhizhen Xu: Hunan Normal University
Qiaoliang Li: Hunan Normal University

Journal of Combinatorial Optimization, 2023, vol. 46, issue 1, No 5, 19 pages

Abstract: Abstract We present an improved approximation algorithm for k-level facility location problem with submodular penalties, the new approximation ratio is 2.9444 for any constant k, which improves the current best approximation ratio 3.314. The central ideas in our results are as follows: first, we restructure the problem as an uncapacitated facility location problem, then we use the primal-dual scheme with greedy augmentation. The key technique of our result is that we change the way of last opening facility set in primal-dual approximation algorithm to get much more tight result for k-level facility location problem with submodular penalties.

Keywords: Submodular penalties; Greedy augmentation; Primal-dual; k-level facility location problem; 90C27; 90C10 (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10878-023-01067-w

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