Abstract
We consider a generalization of the uncapacitated facility location problem that occurs in planning of optical access networks in telecommunications. Clients are connected to open facilities via depth-bounded trees. The total demand of clients served by a tree must not exceed a given tree capacity. We investigate a framework for combining facility location algorithms with a tree-based clustering approach and derive approximation algorithms for several variants of the problem, using techniques for approximating shallow-light Steiner trees via layer graphs, simultaneous approximation of shortest paths and minimum spanning trees, and greedy coverings.
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References
Althaus, E., Funke, S., Har-Peled, S., Könemann, J., Ramos, E.A., Skutella, M.: Approximating k-hop minimum-spanning trees. Operations Research Letters 33(2), 115–120 (2005)
Byrka, J., Aardal, K.: An optimal bifactor approximation algorithm for the metric uncapacitated facility location problem. SIAM Journal on Computing 39(6), 2212–2231 (2010)
Byrka, J., Grandoni, F., Rothvoß, T., Sanità, L.: An improved LP-based approximation for Steiner tree. In: Proceedings of the 42nd ACM Symposium on Theory of Computing, pp. 583–592 (2010)
Charikar, M., Chekuri, C., Cheung, T.-Y., Dai, Z., Goel, A., Guha, S., Li, M.: Approximation algorithms for directed Steiner problems. Journal of Algorithms 33(1), 73–91 (1999)
Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013)
Hassin, R.: Approximation schemes for the restricted shortest path problem. Mathematics of Operations Research 17(1), 36–42 (1992)
Hochbaum, D.S.: Heuristics for the fixed cost median problem. Mathematical Programming 22(1), 148–162 (1982)
Kapoor, S., Sarwat, M.: Bounded-diameter minimum-cost graph problems. Theory of Computing Systems 41(4), 779–794 (2007)
Khuller, S., Raghavachari, B., Young, N.: Balancing minimum spanning trees and shortest-path trees. Algorithmica 14(4), 305–321 (1995)
Kortsarz, G., Peleg, D.: Approximating the weight of shallow Steiner trees. Discrete Applied Mathematics 93(2), 265–285 (1999)
Marathe, M.V., Ravi, R., Sundaram, R., Ravi, S.S., Rosenkrantz, D.J., Hunt, H.B.: Bicriteria network design problems. Journal of Algorithms 28(1), 142–171 (1998)
Maßberg, J., Vygen, J.: Approximation algorithms for a facility location problem with service capacities. ACM Transactions on Algorithms (TALG) 4(4), 50 (2008)
Ravi, R., Sinha, A.: Approximation algorithms for problems combining facility location and network design. Operations Research 54(1), 73–81 (2006)
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Matuschke, J., Bley, A., Müller, B. (2013). Approximation Algorithms for Facility Location with Capacitated and Length-Bounded Tree Connections. In: Bodlaender, H.L., Italiano, G.F. (eds) Algorithms – ESA 2013. ESA 2013. Lecture Notes in Computer Science, vol 8125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40450-4_60
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DOI: https://doi.org/10.1007/978-3-642-40450-4_60
Publisher Name: Springer, Berlin, Heidelberg
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