Approximation Algorithms for Facility Location with Capacitated and Length-Bounded Tree Connections

  • Jannik Matuschke
  • Andreas Bley
  • Benjamin Müller
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8125)

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

  1. 1.
    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)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    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)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    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)Google Scholar
  4. 4.
    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)MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Harks, T., König, F.G., Matuschke, J.: Approximation algorithms for capacitated location routing. Transportation Science 47(1), 3–22 (2013)CrossRefGoogle Scholar
  6. 6.
    Hassin, R.: Approximation schemes for the restricted shortest path problem. Mathematics of Operations Research 17(1), 36–42 (1992)MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Hochbaum, D.S.: Heuristics for the fixed cost median problem. Mathematical Programming 22(1), 148–162 (1982)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Kapoor, S., Sarwat, M.: Bounded-diameter minimum-cost graph problems. Theory of Computing Systems 41(4), 779–794 (2007)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Khuller, S., Raghavachari, B., Young, N.: Balancing minimum spanning trees and shortest-path trees. Algorithmica 14(4), 305–321 (1995)MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Kortsarz, G., Peleg, D.: Approximating the weight of shallow Steiner trees. Discrete Applied Mathematics 93(2), 265–285 (1999)MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    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)MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Maßberg, J., Vygen, J.: Approximation algorithms for a facility location problem with service capacities. ACM Transactions on Algorithms (TALG) 4(4), 50 (2008)Google Scholar
  13. 13.
    Ravi, R., Sinha, A.: Approximation algorithms for problems combining facility location and network design. Operations Research 54(1), 73–81 (2006)MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jannik Matuschke
    • 1
  • Andreas Bley
    • 1
  • Benjamin Müller
    • 1
  1. 1.Institut für MathematikTU BerlinGermany

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