Abstract
We study the bounded metric uncapacitated facility location (bUFL) problem and its two variants, the bounded fault-tolerant facility location (bFTFL) problem and the bounded fault-tolerant facility placement (bFTFP) problem. We propose a unified approximation framework built on the state-of-the-art approximation algorithms for the three unbounded counterparts, leading to a \((2.488 + \epsilon )\)-approximation algorithm for the bUFL problem in the Euclidean plane, a \((1.488+H(n))\)-approximation algorithm for the bUFL problem, a \((1.725+H(n))\)-approximation algorithm for the bFTFL problem, and a \((1.515+H(n))\)-approximation algorithm for the bFTFP problem in a general metric space. We also prove an inapproximability result for all the three bounded facility location problems in a general metric space.
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References
Byrka, J.: An optimal bifactor approximation algorithm for the metric uncapacitated facility location problem. In: Charikar, M., Jansen, K., Reingold, O., Rolim, J.D.P. (eds.) APPROX/RANDOM -2007. LNCS, vol. 4627, pp. 29–43. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74208-1_3
Byrka, J., Srinivasan, A., Swamy, C.: Fault-tolerant facility location: a randomized dependent LP-rounding algorithm. In: Eisenbrand, F., Shepherd, F.B. (eds.) IPCO 2010. LNCS, vol. 6080, pp. 244–257. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13036-6_19
Charikar, M., Guha, S.: Improved combinatorial algorithms for the facility location and \(k\)-median problems. In: FOCS 1999, pp. 378–388 (1999)
Charikar, M., Khuller, S., Mount, D.: Algorithms for facility location problems with outliers. In: SODA 2001, pp. 642–651 (2001)
Chudak, F.A., Shmoys, D.B.: Improved approximation algorithms for the uncapacitated facility location problem. SIAM J. Comput. 33, 1–25 (2004)
Dai, D., Yu, C.: A \((5 + \epsilon )\)-approximation algorithm for minimum weighted dominating set in unit disk graph. Theoret. Comput. Sci. 410, 756–765 (2009)
Dinur, I., Steurer, D.: Analytical approach to parallel repetition. In: STOC 2014, pp. 624–633 (2014)
Guha, S., Meyerson, A., Munagala, K.: A constant factor approximation algorithm for the fault-tolerant facility location problem. J. Algorithms 48, 429–440 (2003)
Hochbaum, D.S.: Heuristics for the fixed cost median problem. Math. Program. 22, 148–162 (1982)
Jain, K., Mahdian, M., Markakis, E., Saberi, A., Vazirani, V.V.: Greedy facility location algorithms analyzed using dual fitting with factor-revealing LP. J. ACM 50, 795–824 (2003)
Jain, K., Mahdian, M., Saberi, A.: A new greedy approach for facility location problems. In: STOC 2002, pp. 731–740 (2002)
Jain, K., Vazirani, V.V.: Approximation algorithms for metric facility location and \(k\)-median problems using the primal-dual schema and Lagrangian relaxation. J. ACM 48, 274–296 (2001)
Jain, K., Vazirani, V.V.: An approximation algorithm for the fault tolerant metric facility location problem. Algorithmica 38, 433–439 (2004)
Johnson, D.S.: Approximation algorithms for combinatorial problems. J. Comput. Syst. Sci. 9, 256–278 (1974)
Korupolu, M.R., Plaxton, C.G., Rajaraman, R.: Analysis of a local search heuristic for facility location problems. J. Algorithms 37, 146–188 (2000)
Krysta, P., Solis-Oba, R.: Approximation algorithms for bounded facility location problems. J. Comb. Optim. 5, 233–247 (2001)
Li, J., Jin, Y.: A PTAS for the weighted unit disk cover problem. In: Halldórsson, M.M., Iwama, K., Kobayashi, N., Speckmann, B. (eds.) ICALP 2015. LNCS, vol. 9134, pp. 898–909. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-47672-7_73
Li, S.: A \(1.488\) approximation algorithm for the uncapacitated facility location problem. Inf. Comput. 222, 45–58 (2013)
Mahdian, M., Ye, Y., Zhang, J.: Approximation algorithms for metric facility location problems. SIAM J. Comput. 36, 411–432 (2006)
Mirchandani, P.B., Francis, R.L.: Discrete Location Theory. Wiley, New York (1990)
Rajagopalan, S., Vazirani, V.V.: Primal-dual RNC approximation algorithms for set cover and covering integer programs. SIAM J. Comput. 28, 525–540 (1998)
Rybicki, B., Byrka, J.: Improved approximation algorithm for fault-tolerant facility placement. In: Bampis, E., Svensson, O. (eds.) WAOA 2014. LNCS, vol. 8952, pp. 59–70. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-18263-6_6
Shmoys, D.B., Tardos, É., Aardal, K.: Approximation algorithms for facility location problems (extended abstract). In: STOC 1997, pp. 265–274 (1997)
Swamy, C., Shmoys, D.B.: Fault-tolerant facility location. ACM Trans. Algorithms 4, 1–27 (2008)
Vazirani, V.V.: Approximation Algorithms. Springer, Berlin (2003). https://doi.org/10.1007/978-3-662-04565-7
Weng, K.: Approximation algorithm for uniform bounded facility location problem. J. Comb. Optim. 26, 284–291 (2013)
Xu, G., Xu, J.: An improved approximation algorithm for uncapacitated facility location problem with penalties. J. Comb. Optim. 17, 424–436 (2008)
Xu, S., Shen, H.: The fault-tolerant facility allocation problem. In: Dong, Y., Du, D.-Z., Ibarra, O. (eds.) ISAAC 2009. LNCS, vol. 5878, pp. 689–698. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-10631-6_70
Yan, L., Chrobak, M.: Approximation algorithms for the fault-tolerant facility placement problem. Inf. Process. Lett. 111, 545–549 (2011)
Yan, L., Chrobak, M.: LP-rounding algorithms for the fault-tolerant facility placement problem. J. Discret. Algorithms 33, 93–114 (2015)
Acknowledgements
This research is partially supported by NSERC Canada, NNSF of China (Grant No. 61672323), the K. C. Wong Magna Foundation of Ningbo University, the China Scholarship Council (Grant No. 201408330402), and the Ningbo Natural Science Foundation (Grant No. 2016A610078).
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Luo, W., Su, B., Xu, Y., Lin, G. (2018). An Approximation Framework for Bounded Facility Location Problems. In: Wang, L., Zhu, D. (eds) Computing and Combinatorics. COCOON 2018. Lecture Notes in Computer Science(), vol 10976. Springer, Cham. https://doi.org/10.1007/978-3-319-94776-1_30
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