Zoya Svitkina
Abstract
We study the lower-bounded facility location problem which generalizes the classical uncapacitated facility location problem in that it comes with lower bound constraints for the number of clients assigned to a facility in the case that this facility is opened. This problem was introduced independently in the papers by Karger and Minkoff [2000] and by Guha et al. [2000], both of which give bicriteria approximation algorithms for it. These bicriteria algorithms come within a constant factor of the optimal solution cost, but they also violate the lower bound constraints by a constant factor. Our result in this article is the first true approximation algorithm for the lower-bounded facility location problem which respects the lower bound constraints and achieves a constant approximation ratio for the objective function. The main technical idea for the design of the algorithm is a reduction to the capacitated facility location problem, which has known constant-factor approximation algorithms.
- Arya, V., Garg, N., Khandekar, R., Meyerson, A., Munagala, K., and Pandit, V. 2004. Local search heuristics for k-median and facility location problems. SIAM J. Comput. 33, 3, 544--562. Google Scholar
Digital Library
- Byrka, J. 2007. An optimal bifactor approximation algorithm for the metric uncapacitated facility location problem. In Proceedings of the 10th International Workshop on Approximation Algorithms for Combinatorial Optimization (APPROX). 29--43. Google ScholarDigital Library
- Charikar, M. and Guha, S. 2005. Improved combinatorial algorithms for facility location problems. SIAM J. Comput. 34, 4, 803--824. Google ScholarDigital Library
- Chudak, F. and Shmoys, D. 1999. Improved approximation algorithms for a capacitated facility location problem. In Proceedings of the 10th ACM Symposium on Discrete Algorithms. 875--876. Google ScholarDigital Library
- Chudak, F. and Shmoys, D. 2003. Improved approximation algorithms for the uncapacitated facility location problem. SIAM J. Comput. 33, 1, 1--25. Google ScholarDigital Library
- Chudak, F. and Williamson, D. 2005. Improved approximation algorithms for capacitated facility location problems. Math. Program. 102, 2, 207--222. Google ScholarDigital Library
- Guha, S., Meyerson, A., and Munagala, K. 2000. Hierarchical placement and network design problems. In Proceedings of the 41st IEEE Symposium on Foundations of Computer Science. 603. Google ScholarDigital Library
- Guha, S., Meyerson, A., and Munagala, K. 2001. A constant factor approximation for the single sink edge installation problems. In Proceedings of the 33rd ACM Symposium on Theory of Computing. 383--388. Google ScholarDigital Library
- Hajiaghayi, M. T., Mahdian, M., and Mirrokni, V. S. 2003. The facility location problem with general cost functions. Netw. 42, 42--47.Google ScholarCross Ref
- Jain, K., Mahdian, M., and Saberi, A. 2002. A new greedy approach for facility location problems. In Proceedings of the 34th ACM Symposium on Theory of Computing. 731--740. Google ScholarDigital Library
- Jain, K. and Vazirani, V. V. 2001. Approximation algorithms for metric facility location and k-median problems using the primal-dual schema and lagrangian relaxation. J. ACM 48, 2, 274--296. Google ScholarDigital Library
- Karger, D. R. and Minkoff, M. 2000. Building steiner trees with incomplete global knowledge. In Proceedings of the 41st IEEE Symposium on Foundations of Computer Science. 613. Google ScholarDigital Library
- Korupolu, M. R., Plaxton, C. G., and Rajaraman, R. 2000. Analysis of a local search heuristic for facility location problems. J. Algor. 37, 1, 146--188. Google ScholarDigital Library
- Lim, A., Wang, F., and Xu, Z. 2006. A transportation problem with minimum quantity commitment. Transport. Sci. 40, 1, 117--129. Google ScholarDigital Library
- Mahdian, M. and Pál, M. 2003. Universal facility location. In Proceedings of the European Symposium on Algorithms. 409--421.Google Scholar
- Mahdian, M., Ye, Y., and Zhang, J. 2003. A 2-approximation algorithm for the soft-capacitated facility location problem. In Proceedings of the 6th International Workshop on Approximation Algorithms for Combinatorial Optimization (APPROX). 129--140.Google Scholar
- Pal, M., Tardos, E., and Wexler, T. 2001. Facility location with nonuniform hard capacities. In Proceedings of the 42nd IEEE Symposium on Foundations of Computer Science. 329. Google ScholarDigital Library
- Shmoys, D. B., Tardos, E., and Aardal, K. 1997. Approximation algorithms for facility location problems. In Proceedings of the 29th ACM Symposium on Theory of Computing. 265--274. Google ScholarDigital Library
- Sviridenko, M. 2002. An improved approximation algorithm for the metric uncapacitated facility location problem. In Proceedings of the Conference on Integer Programming and Combinatorial Optimization (IPCO). 240--257. Google ScholarDigital Library
- Vygen, J. 2007. From stars to comets: Improved local search for universal facility location. Oper. Res. Lett. 35, 4, 427--433. Google ScholarDigital Library
- Zhang, J., Chen, B., and Ye, Y. 2005. A multiexchange local search algorithm for the capacitated facility location problem. Math. Oper. Res. 30, 2, 389--403. Google ScholarDigital Library
Index Terms
- Lower-bounded facility location
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