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 [2], we obtain a combinatorial algorithm with a performance factor of 3.27 for any k ≥ 2, thus improving the previous bound of 4.56. 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 δ. The values of h(k) can be easily computed with an arbitrary accuracy: h(2) ≈ 2.4211, h(3) ≈ 2.8446, h(4) ≈ 3.0565, h(5) ≈ 3.1678 and so on. Thus, for the cases of k = 2 and k = 3 the second combinatorial algorithm ensures an approximation factor significantly better than 3, which is currently the best approximation ratio for the k-level problem provided by the non-combinatorial algorithm due to Aardal, Chudak, and Shmoys [1].
Research was partially supported by the Russian Foundation for Basic Research, project codes 01-01-00786, 02-01-01153, by INTAS, project code 00-217, and by the Programme “Universities of Russia”, project code UR.04.01.012.
Research supported in part by NSF grant DMI-0231600.
Research supported in part by NSF grant DMI-0231600.
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Ageev, A., Ye, Y., Zhang, J. (2003). Improved Combinatorial Approximation Algorithms for the k-Level Facility Location Problem. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds) Automata, Languages and Programming. ICALP 2003. Lecture Notes in Computer Science, vol 2719. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45061-0_13
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DOI: https://doi.org/10.1007/3-540-45061-0_13
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