Abstract
We study Connected Facility Location problems. We are given a connected graph G=(V,E) with nonnegative edge cost c e for each edge e∈E, a set of clients D⊆V such that each client j∈D has positive demand d j and a set of facilities F⊆V each has nonnegative opening cost f i and capacity to serve all client demands. The objective is to open a subset of facilities, say \(\hat{F}\) , to assign each client j∈D to exactly one open facility i(j) and to connect all open facilities by a Steiner tree T such that the cost \(\sum_{i\in \hat{F}}f_{i}+\sum_{j\in D}d_{j}c_{i(j)j}+M\sum_{e\in T}c_{e}\) is minimized for a given input parameter M≥1. We propose a LP-rounding based 8.29 approximation algorithm which improves the previous bound 8.55 (Swamy and Kumar in Algorithmica, 40:245–269, 2004). We also consider the problem when opening cost of all facilities are equal. In this case we give a 7.0 approximation algorithm.
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References
Goemans MX, Williamson DP (1995) A general approximation technique for constrained forest problems. SIAM J Comput 24:296–317
Grandoni F, Italiano G (2006) Improved approximation for single-sink buy-at-bulk. In: Proceedings of 17th international symposium on algorithms and computation (ISAAC), pp 111–120
Guha S, Khuller S (1998) Greedy strikes back: Improved facility location algorithms. In: Proceedings of 9th annual ACM-SIAM symposium on discrete algorithms, pp 649–657
Gupta A, Kleinberg JM, Kumar A, Rastogi R, Yener B (2001) Provisioning a virtual private network: a network design problem for multicommodity flow. In: Proceedings of 33rd ACM symposium on theory of computing, pp 389–398
Gupta A, Kumar A, Roughgarden T (2003) Simpler and better approximation algorithms for network design. In: Proceedings of 35th annual ACM symposium on theory of computing, New York, NY, USA, pp 365–372
Jain K, Vazirani VV (2001) Approximation algorithms for metric facility location and k-median problems using the primal-dual schema and Lagrangian relaxation. J ACM 48:274–296
Jothi R, Raghavachari B (2004) Improved approximation algorithms for the single-sink buy-at-bulk network design problems. In: Proceedings of 9th Scandinavian workshop on algorithm theory (SWAT), pp 336–348
Karger DR, Minkoff M (2000) Building steiner trees with incomplete global knowledge. In: Proceedings of 41st annual IEEE symposiam on foundations of computer science, Washington, DC, USA, pp 613–623
Korupolu MR, Plaxton CG, Rajaraman R (1998) Analysis of a local search heuristic for facility location problems. In: Proceedings of 9th annual ACM-SIAM symposium on discrete algorithms, pp 1–10
Lin J, Vitter JS (1992) ε-approximations with minimum packing constraint violation. In: Proceedings of 24th ACM symposium on theory of computing, pp 771–782
Mahdian M, Ye Y, Zhang J (2002) Improved approximation algorithms for metric facility location problems. In: Proceedings of 5th international Workshop on approximation algorithms for combinatorial optimization, pp 229–242
Robins G, Zelikovsky A (2007) Improved Steiner tree approximation in graphs. In: Proceedings of 11th annual ACM-SIAM symposium on discrete algorithms, pp 770–779
Shmoys DB, Tardos É, Aardal K (1997) Approximation algorithms for facility location problems (extended abstract). In: Proceedings of 29th ACM symposium on theory of computing, pp 265–274
Swamy C, Kumar A (2002) Primal-dual algorithms for connected facility location problems. In: Proceedings of 5th APPROX. LNCS, vol. 2462, pp 256–269
Swamy C, Kumar A (2004) Primal-dual algorithms for connected facility location problems. Algorithmica 40:245–269
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Hasan, M.K., Jung, H. & Chwa, KY. Approximation algorithms for connected facility location problems. J Comb Optim 16, 155–172 (2008). https://doi.org/10.1007/s10878-007-9130-0
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DOI: https://doi.org/10.1007/s10878-007-9130-0