NDLI: Improved Combinatorial Approximation Algorithms for the k-Level Facility Location Problem

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Ageev, Alexander Zhang, Jiawei Ye, Yinyu
Copyright Year	2004
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].
Starting Page	207
Ending Page	217
Page Count	11
File Format	PDF
ISSN	08954801
DOI	10.1137/S0895480102417215
e-ISSN	10957146
Journal	SIAM Journal on Discrete Mathematics (SJDMEC)
Issue Number	1
Volume Number	18
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-08-01
Access Restriction	Subscribed
Subject Keyword	polynomial-time reduction Analysis of algorithms and problem complexity approximation algorithm performance guarantee Approximation algorithms Analysis of algorithms Discrete location and assignment Combinatorial optimization facility location
Content Type	Text
Resource Type	Article
Subject	Mathematics

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