Abstract
We consider the incremental version of the k-Facility Location Problem, which is a common generalization of the facility location and the k-median problems. The objective is to produce an incremental sequence of facility sets F 1⊆F 2⊆⋅⋅⋅⊆F n , where each F k contains at most k facilities. An incremental facility sequence or an algorithm producing such a sequence is called c -competitive if the cost of each F k is at most c times the optimum cost of corresponding k-facility location problem, where c is called competitive ratio. In this paper we present two competitive algorithms for this problem. The first algorithm produces competitive ratio 8α, where α is the approximation ratio of k-facility location problem. By recently result (Zhang, Theor. Comput. Sci. 384:126–135, 2007), we obtain the competitive ratio \(16+8\sqrt{3}+\epsilon\) . The second algorithm has the competitive ratio Δ+1, where Δ is the ratio between the maximum and minimum nonzero interpoint distances. The latter result has its self interest, specially for the small metric space with Δ≤8α−1.
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This research is supported by the Specialized Research Foundation for the Doctoral Program of Higher Education of China, Grant No. 200806141084, and Science Foundation of UESTC for Youths.
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Dai, W., Zeng, X. Incremental Facility Location Problem and Its Competitive Algorithms. J Comb Optim 20, 307–320 (2010). https://doi.org/10.1007/s10878-009-9219-8
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DOI: https://doi.org/10.1007/s10878-009-9219-8