Improved Approximation Algorithm for Fault-Tolerant Facility Placement

  • Bartosz RybickiEmail author
  • Jaroslaw Byrka
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8952)


We consider the Fault-Tolerant Facility Placement problem (\(FTFP\)), which is a generalization of the classical Uncapacitated Facility Location problem (\(UFL\)). In the \(FTFP\) problem we have a set of clients \(C\) and a set of facilities \(F\). Each facility \(i \in F\) can be opened many times. For each opening of facility \(i\) we pay \(f_i \ge 0\). Our goal is to connect each client \(j \in C\) with \(r_j \ge 1\) open facilities in a way that minimizes the total cost of open facilities and established connections.

In a series of recent papers \(FTFP\) was essentially reduced to Fault-Tolerant Facility Location problem (\(FTFL\)) and then to \(UFL\) showing it could be approximated with ratio \(1.575\). In this paper we show that \(FTFP\) can actually be approximated even better. We consider approximation ratio as a function of \(r = min_{j \in C}~r_j\) (minimum requirement of a client). With increasing \(r\) the approximation ratio of our algorithm \(\lambda _r\) converges to one. Furthermore, for \(r > 1\) the value of \(\lambda _r\) is less than 1.463 (hardness of approximation of \(UFL\)). We also show a lower bound of 1.278 for the approximability of the \(FTFL\) for arbitrary \(r\). Already for \(r > 3\) we obtain that \(FTFP\) can be approximated with ratio 1.275, showing that under standard complexity theoretic assumptions \(FTFP\) is strictly better approximable than \(FTFL\).


  1. 1.
    Li, S.: A 1.488 approximation algorithm for the uncapacitated facility location problem. Inf. Comput. 222, 45–58 (2013)CrossRefzbMATHGoogle Scholar
  2. 2.
    Jain, K., Mahdian, M., Saberi, A.: A new greedy approach for facility location problems. In: STOC, pp. 731–740 (2002)Google Scholar
  3. 3.
    Dinur, I., Steurer, D.: Analytical approach to parallel repetition. In: STOC, pp. 624–633 (2014)Google Scholar
  4. 4.
    Sviridenko, M.: 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
  5. 5.
    Byrka, J., Aardal, K.: An optimal bifactor approximation algorithm for the metric uncapacitated facility location problem. SIAM J. Comput. 39(6), 2212–2231 (2010)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Shmoys, D., Tardos, E., Aardal, K.: Approximation algorithms for facility location problems (Extended abstract). In: STOC, pp. 265–274 (1997)Google Scholar
  7. 7.
    Yan, L.: Approximation algorithms for the Fault-Tolerant facility placement problem, Ph.D. ThesisGoogle Scholar
  8. 8.
    Yan, L., Chrobak, M.: Approximation algorithms for the Fault-Tolerant facility placement problem. Inf. Process. Lett. 111(11), 545–549 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Feige, U.: A threshold of ln n for approximating set-cover. In: 28th ACM Symposium on Theory of Computing, pp. 314–318 (1996)Google Scholar
  10. 10.
    Gandhi, R., Khuller, S., Parthasarathy, S., Srinivasan, A.: Dependent rounding and its applications to approximation algorithms. J. ACM 53(3), 324–360 (2006)CrossRefMathSciNetGoogle Scholar
  11. 11.
    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
  12. 12.
    Swamy, C., Shmoys, D.: Fault-Tolerant facility location. ACM Trans. Algorithms 4(4), 1–27 (2008)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Guha, S., Khuller, S.: Greedy strikes back: improved facility location algorithms. In: Proceedings of the 9th ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 228–248. SIAM, Philadelphia (1998)Google Scholar
  14. 14.
    Guha, S., Meyerson, A., Munagala, K.: Improved algorithms for fault tolerant facility location. In: SODA, pp. 636–641 (2001)Google Scholar
  15. 15.
    Rybicki, B., Byrka, J.: Improved approximation algorithm for Fault-Tolerant Facility Placement. CoRR abs/1311.6615 (2013)Google Scholar
  16. 16.
    Chudak, F., Shmoys, D.: Improved approximation algorithms for the uncapacitated facility location problem. SIAM J. Comput. 33(1), 1–25 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  17. 17.
    Byrka, J., Ghodsi, M., Srinivasan, A.: LP-rounding algorithms for facility-location problems. CoRR abs/1007.3611 (2010)Google Scholar
  18. 18.
    Yan, L., Chrobak, M.: LP-rounding Algorithms for the Fault-Tolerant Facility Placement Problem. CoRR abs/1205.1281 (2012)Google Scholar
  19. 19.
    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

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Institute of Computer ScienceUniversity of WrocławWrocławPoland

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