A Multiexchange Local Search Algorithm for the Capacitated Facility Location Problem

We present a multiexchange local search algorithm for approximating the capacitated facility location problem (CFLP), where a new local improvement operation is introduced that possibly exchanges multiple facilities simultaneously. We give a tight analysis for our algorithm and show that the performance guarantee of the algorithm is between 3+2v2-e and 3+2v2+e for any given constant e>0. The previously known best approximation ratio for the CFLP is 7.88, as shown by Mahdian and PAil (2003. Universal facility location.Proc. 11th Annual Eur. Sympos. Algorithms (ESA), 409--421), based on the operations proposed by PAil et al. (2001. Facility location with hard capacities.Proc. 42nd IEEE Sympos. Foundations Comput. Sci. (FOCS), 329--338). Our upper bound 3+2v2+e also matches the best-known ratio, obtained by Chudak and Williamson (1999.Improved approximation algorithm for capacitated facility location problems. Proc. 7th Conf. Integer Programming Combin. Optim. (IPCO), 99--113), for the CFLP with uniform capacities. In order to obtain the tight bound of our new algorithm, we make interesting use of the notion of exchange graph of PAil et al. and techniques from the area of parallel machine scheduling.

[1]  Samir Khuller,et al.  Algorithms for facility location problems with outliers , 2001, SODA '01.

[2]  Jiawei Zhang,et al.  Approximation algorithms for facility location problems , 2004 .

[3]  Mohammad Mahdian,et al.  Improved Approximation Algorithms for Metric Facility Location Problems , 2002, APPROX.

[4]  Mohammad Mahdian,et al.  Universal Facility Location , 2003, ESA.

[5]  Jiawei Zhang,et al.  Improved Combinatorial Approximation Algorithms for the k-Level Facility Location Problem , 2004, SIAM J. Discret. Math..

[6]  Chaitanya Swamy,et al.  Fault-tolerant facility location , 2003, SODA '03.

[7]  George L. Nemhauser,et al.  The uncapacitated facility location problem , 1990 .

[8]  Karen Aardal,et al.  A 3-Approximation Algorithm for the k-Level Uncapacitated Facility Location Problem , 1999, Inf. Process. Lett..

[9]  Mohammad Mahdian,et al.  A 2-Approximation Algorithm for the Soft-Capacitated Facility Location Problem , 2003, RANDOM-APPROX.

[10]  Rajmohan Rajaraman,et al.  Analysis of a local search heuristic for facility location problems , 2000, SODA '98.

[11]  Samir Khuller,et al.  The Capacitated K-Center Problem , 2000, SIAM J. Discret. Math..

[12]  Amin Saberi,et al.  A new greedy approach for facility location problems , 2002, STOC '02.

[13]  Samir Khuller,et al.  Greedy strikes back: improved facility location algorithms , 1998, SODA '98.

[14]  David P. Williamson,et al.  Improved approximation algorithms for capacitated facility location problems , 1999, IPCO.

[15]  Jiawei Zhang.  Approximating the two-level facility location problem via a quasi-greedy approach , 2004, SODA '04.

[16]  Fabián A. Chudak,et al.  Improved Approximation Algorithms for the Uncapacitated Facility Location Problem , 2003, SIAM J. Comput..

[17]  Jiawei Zhang,et al.  A Multi-exchange Local Search Algorithm for the Capacitated Facility Location Problem: (Extended Abstract) , 2004, IPCO.

[18]  David B. Shmoys,et al.  Approximation algorithms for facility location problems , 2000, APPROX.

[19]  Alfred A. Kuehn,et al.  A Heuristic Program for Locating Warehouses , 1963 .

[20]  Kamesh Munagala,et al.  Local search heuristic for k-median and facility location problems , 2001, STOC '01.

[21]  Sudipto Guha,et al.  Improved algorithms for fault tolerant facility location , 2001, SODA '01.