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Improved Approximation Algorithms for Constrained Fault-Tolerant Resource Allocation

(Extended Abstract)
  • Kewen Liao
  • Hong Shen
  • Longkun Guo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8070)

Abstract

In Constrained Fault-Tolerant Resource Allocation (FTRA) problem, we are given a set of sites containing facilities as resources and a set of clients accessing these resources. Each site i can open at most R i facilities with opening cost f i . Each client j requires an allocation of r j open facilities and connecting j to any facility at site i incurs a connection cost c ij . The goal is to minimize the total cost of this resource allocation scenario. FTRA generalizes the Unconstrained Fault-Tolerant Resource Allocation (FTRA  ∞ ) [10] and the classical Fault-Tolerant Facility Location (FTFL) [7] problems: for every site i, FTRA  ∞  does not have the constraint R i , whereas FTFL sets R i  = 1. These problems are said to be uniform if all r j ’s are the same, and general otherwise. For the general metric FTRA, we first give an LP-rounding algorithm achieving an approximation ratio of 4. Then we show the problem reduces to FTFL, implying the ratio of 1.7245 from [2]. For the uniform FTRA, we provide a 1.52-approximation primal-dual algorithm in O(n 4) time, where n is the total number of sites and clients.

Keywords

Facility Location Facility Location Problem Open Facility Connection Cost Uncapacitated Facility Location Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    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)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    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)CrossRefGoogle Scholar
  3. 3.
    Chudak, F.A., Shmoys, D.B.: Improved approximation algorithms for the uncapacitated facility location problem. SIAM J. Comput. 33(1), 1–25 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Guha, S., Khuller, S.: Greedy strikes back: Improved facility location algorithms. Journal of Algorithms 31(21), 228–248 (1999)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Guha, S., Meyerson, A., Munagala, K.: A constant factor approximation algorithm for the fault-tolerant facility location problem. J. Algorithms 48(2), 429–440 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Jain, K., Mahdian, M., Markakis, E., Saberi, A., Vazirani, V.V.: Greedy facility location algorithms analyzed using dual fitting with factor-revealing LP. Journal of the ACM 50(6), 795–824 (2003)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Jain, K., Vazirani, V.V.: An approximation algorithm for the fault tolerant metric facility location problem. In: Jansen, K., Khuller, S. (eds.) APPROX 2000. LNCS, vol. 1913, pp. 177–182. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  8. 8.
    Jain, K., Vazirani, V.V.: Approximation algorithms for metric facility location and k-median problems using the primal-dual schema and Lagrangian relaxation. Journal of the ACM 48(2), 274–296 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Li, S.: A 1.488 approximation algorithm for the uncapacitated facility location problem. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011, Part II. LNCS, vol. 6756, pp. 77–88. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  10. 10.
    Liao, K., Shen, H.: Unconstrained and constrained fault-tolerant resource allocation. In: Fu, B., Du, D.-Z. (eds.) COCOON 2011. LNCS, vol. 6842, pp. 555–566. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  11. 11.
    Mahdian, M., Ye, Y., Zhang, J.: Approximation algorithms for metric facility location problems. SIAM J. Comput. 36(2), 411–432 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Shmoys, D.B., Tardos, E., Aardal, K.: Approximation algorithms for facility location problems. In: Proceedings of the 29th Annual ACM Symposium on Theory of Computing (STOC), El Paso, Texas, USA, May 4-6, pp. 265–274. ACM, New York (1997)Google Scholar
  13. 13.
    Sviridenko, M.I.: An improved approximation algorithm for the metric uncapacitated facility location problem. In: Cook, W.J., Schulz, A.S. (eds.) IPCO 2002. LNCS, vol. 2337, pp. 240–257. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  14. 14.
    Swamy, C., Shmoys, D.B.: Fault-tolerant facility location. ACM Trans. Algorithms 4(4), 1–27 (2008)MathSciNetCrossRefGoogle Scholar
  15. 15.
    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)CrossRefGoogle Scholar
  16. 16.
    Yan, L., Chrobak, M.: Approximation algorithms for the fault-tolerant facility placement problem. Information Processing Letters 111(11), 545 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    Yan, L., Chrobak, M.: New results on the fault-tolerant facility placement problem. Technical report (2011), http://arxiv.org/abs/1108.5471, CoRR
  18. 18.
    Yan, L., Chrobak, M.: Lp-rounding algorithms for the fault-tolerant facility placement problem. Technical report (2012). In: Spirakis, P.G., Serna, M. (eds.) CIAC 2013. LNCS, vol. 7878, pp. 370–381. Springer, Heidelberg (2013)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Kewen Liao
    • 1
  • Hong Shen
    • 1
    • 2
  • Longkun Guo
    • 2
  1. 1.School of Computer ScienceThe University of AdelaideAdelaideAustralia
  2. 2.School of Computer and Information TechnologySun Yat-sen UniversityGuangzhouChina

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