A 2-Approximation Algorithm for the Soft-Capacitated Facility Location Problem

This paper is divided into two parts. In the first part of this paper, we present a 2-approximation algorithm for the soft-capacitated facility location problem. This achieves the integrality gap of the natural LP relaxation of the problem. The algorithm is based on an improved analysis of an algorithm for the linear facility location problem, and a bifactor approximate-reduction from this problem to the soft-capacitated facility location problem. We will define and use the concept of bifactor approximate reductions to improve the approximation factor of several other variants of the facility location problem. In the second part of the paper, we present an alternative analysis of the authors’ 1.52-approximation algorithm for the uncapacitated facility location problem, using a single factor-revealing LP. This answers an open question of [16]Furthermore, this analysis, combined with a recent result of Thorup [21] shows that our algorithm can be implemented in quasi-linear time, achieving the best known approximation factor in the best possible running time.

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

[2]  Ravi Ramamoorthi,et al.  Integrated Logistics: Approximation Algorithms Combining Facility Location and Network Design , 2002, IPCO.

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

[4]  Fabián A. Chudak,et al.  Improved approximation algorithms for a capacitated facility location problem , 1999, SODA '99.

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

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

[7]  Mikkel Thorup.  Quick k-Median, k-Center, and Facility Location for Sparse Graphs , 2001, ICALP.

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

[9]  Evangelos Markakis,et al.  A Greedy Facility Location Algorithm Analyzed Using Dual Fitting , 2001, RANDOM-APPROX.

[10]  Vijay V. Vazirani,et al.  Approximation algorithms for metric facility location and k-Median problems using the primal-dual schema and Lagrangian relaxation , 2001, JACM.

[11]  Maxim Sviridenko.  An Improved Approximation Algorithm for the Metric Uncapacitated Facility Location Problem , 2002, IPCO.

[12]  Fabián A. Chudak.  Improved Approximation Algorithms for Uncapitated Facility Location , 1998, IPCO.

[13]  Alex Zelikovsky,et al.  Improved Steiner tree approximation in graphs , 2000, SODA '00.

[14]  Mikkel Thorup,et al.  Quick k-Median, k-Center, and Facility Location for Sparse Graphs , 2001, SIAM J. Comput..

[15]  Robin Milner,et al.  On Observing Nondeterminism and Concurrency , 1980, ICALP.

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

[17]  Sudipto Guha,et al.  Improved combinatorial algorithms for the facility location and k-median problems , 1999, 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039).

[18]  Sudipto Guha,et al.  Hierarchical placement and network design problems , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[19]  Bhaba R. Sarker,et al.  Discrete location theory , 1991 .

[20]  David R. Karger,et al.  Building Steiner trees with incomplete global knowledge , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[21]  Mikkel Thorup,et al.  Quick and good facility location , 2003, SODA '03.

[22]  Klaus Jansen,et al.  Approximation Algorithms for Combinatorial Optimization , 2000 .

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

[24]  K. Holmberg.  Solving the staircase cost facility location problem with decomposition and piecewise linearization , 1994 .

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

[26]  V. Mirrokni,et al.  The Facility Location Problem with Concave Cost Functions , 2002 .

[27]  Éva Tardos,et al.  Approximation algorithms for facility location problems (extended abstract) , 1997, STOC '97.

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

[29]  Kamesh Munagala,et al.  Local Search Heuristics for k-Median and Facility Location Problems , 2004, SIAM J. Comput..