Abstract
This paper deals with a single allocation problem in hub-and-spoke networks. We handle the case that all the nodes are embedded in a 2-dimensional plane and a transportation cost (per unit flow) is proportional to Euclidean distance. We propose a randomized (1 + 2/π)-approximation algorithm based on a linear relaxation problem and a dependent rounding procedure.
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References
Adams, W.P., Sherali, H.D.: A tight linearization and an algorithm for zero-one quadratic programming problems. Management Science 32, 1274–1290 (1986)
Bertsimas, D., Teo, C., Vohra, R.: On dependent randomized rounding algorithms. Operations Research Letters 24, 105–114 (1999)
Bryan, D.L., O’Kelly, M.E.: Hub-and-spoke networks in air transportation: an analytical review. Journal of Regional Science 39, 275–295 (1999)
Burkard, R.E., Klinz, B., Rudolf, R.: Perspectives of Monge properties in optimization. Discrete Applied Mathematics 70, 95–161 (1996)
Campbell, J.F.: Integer programming formulations of discrete hub location problems. European Journal of Operational Research 72, 387–405 (1994)
Chekuri, C., Khanna, S., Naor, J., Zosin, L.: A linear programming formulation and approximation algorithms for the metric labeling problem. SIAM Journal on Discrete Mathematics 18, 608–625 (2005)
Ge, D., Ye, Y., Zhang, J.: The Fixed-Hub Single Allocation Problem: A Geometric Rounding Approach (October 2007) (manuscript)
Hamacher, H.W., Labbé, M., Nickel, S., Sonneborn, T.: Adapting polyhedral properties from facility to hub location problems. Discrete Applied Mathematics 145, 104–116 (2004)
Iwasa, M., Saito, H., Matsui, T.: Approximation Algorithms for the Single Allocation Problem in Hub-and-Spoke Networks and Related Metric Labeling Problems. Discrete Applied Mathematics 157, 2078–2088 (2009)
Labbé, M., Yaman, H.: Projecting the flow variables for hub location problems. Networks 44, 84–93 (2004)
Labbé, M., Yaman, H., Gourdin, E.: A branch and cut algorithm for hub location problems with single assignment. Mathematical Programming 102, 371–405 (2005)
O’Kelly, M.E.: A quadratic integer program for the location of interacting hub facilities. European Journal of Operational Research 32, 393–404 (1987)
Saito, H., Fujie, T., Matsui, T., Matuura, S.: The Quadratic semi-assignment polytope. Discrete Optimization 6, 37–50 (2009)
Saito, H., Matuura, S., Matsui, T.: A linear relaxation for hub network design problems. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E85-A, 1000–1005 (2002)
Sohn, J., Park, S.: A linear program for the two-hub location problem. European Journal of Operational Research 100, 617–622 (1997)
Sohn, J., Park, S.: The single allocation problem in the interacting three-hub network. Networks 35, 17–25 (2000)
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Ando, R., Matsui, T. (2011). Algorithm for Single Allocation Problem on Hub-and-Spoke Networks in 2-Dimensional Plane. In: Asano, T., Nakano, Si., Okamoto, Y., Watanabe, O. (eds) Algorithms and Computation. ISAAC 2011. Lecture Notes in Computer Science, vol 7074. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25591-5_49
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DOI: https://doi.org/10.1007/978-3-642-25591-5_49
Publisher Name: Springer, Berlin, Heidelberg
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