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- W2053751186 abstract "In this paper we present improved combinatorial approximation algorithms for the k-level facility location problem. First, by modifying the path reduction developed in [A. A. Ageev, Oper. Res. Lett., 30 (2002), pp. 327--332], we obtain a combinatorial algorithm with a performance factor of 3.27 for any k ge 2, thus improving the previous bound of 4.56 achieved by a combinatorial algorithm. Then we develop another combinatorial algorithm that has a better performance guarantee and uses the first algorithm as a subroutine. The latter algorithm can be recursively implemented and achieves a guarantee factor h(k), where h(k) is strictly less than 3.27 for any k and tends to 3.27 as k goes to $infty$. The values of h(k) can be easily computed with an arbitrary accuracy: h(2)approx 2.4211, h(3)approx 2.8446, h(4)approx 3.0565, h(5)approx 3.1678, and so on. Thus, for the cases of k=2 and k=3 the second combinatorial algorithm ensures an approximation factor substantially better than 3, which is currently the best approximation ratio for the k-level problem provided by the noncombinatorial algorithm due to Aardal, Chudak, and Shmoys [Inform. Process. Lett., 72 (1999), pp. 161--167]." @default.
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- W2053751186 date "2004-01-01" @default.
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- W2053751186 title "Improved Combinatorial Approximation Algorithms for the <i>k</i>-Level Facility Location Problem" @default.
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- W2053751186 doi "https://doi.org/10.1137/s0895480102417215" @default.
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