An approximation algorithm for k-facility location problem with linear penalties using local search scheme

Yishui Wang (), Dachuan Xu (), Donglei Du () and Chenchen Wu ()
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Yishui Wang: Beijing University of Technology
Dachuan Xu: Beijing University of Technology
Donglei Du: University of New Brunswick
Chenchen Wu: Tianjin University of Technology

Journal of Combinatorial Optimization, 2018, vol. 36, issue 1, No 20, 264-279

Abstract: Abstract In this paper, we consider an extension of the classical facility location problem, namely k-facility location problem with linear penalties. In contrast to the classical facility location problem, this problem opens no more than k facilities and pays a penalty cost for any non-served client. We present a local search algorithm for this problem with a similar but more technical analysis due to the extra penalty cost, compared to that in Zhang (Theoretical Computer Science 384:126–135, 2007). We show that the approximation ratio of the local search algorithm is $$2 + 1/p + \sqrt{3+ 2/p+ 1/p^2} + \epsilon $$ 2 + 1 / p + 3 + 2 / p + 1 / p 2 + ϵ , where $$p \in {\mathbb {Z}}_+$$ p ∈ Z + is a parameter of the algorithm and $$\epsilon >0$$ ϵ > 0 is a positive number.

Keywords: Approximation algorithm; k-facility location; Local search; Linear penalties (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10878-016-0080-2

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