Offline and Online Facility Leasing

  • Chandrashekhar Nagarajan
  • David P. Williamson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5035)


We study the problem of leasing facilities over time, following the general infrastructure leasing problem framework introduced by Anthony and Gupta [1]. If there are K different lease types, Anthony and Gupta give an O(K)-approximation algorithm for the problem. We are able to improve this to a 3-approximation algorithm by using a variant of the primal-dual facility location algorithm of Jain and Vazirani [5]. We also consider the online version of the facility leasing problem, in which the clients to be served arrive over time and are not known in advance. This problem generalizes both the online facility location problem (introduced by Meyerson [6]) and the parking permit problem (also introduced by Meyerson [7]). We give a deterministic algorithm for the problem that is O(Klogn)-competitive. To achieve our result, we modify an O(logn)-competitive algorithm of Fotakis [2] for the online facility location problem.


Facility Location Competitive Ratio Dual Variable Facility Location Problem Competitive Algorithm 
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  1. 1.
    Anthony, B.M., Gupta, A.: Infrastructure leasing problems. In: Fischetti, M., Williamson, D.P. (eds.) IPCO 2007. LNCS, vol. 4513, pp. 424–438. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  2. 2.
    Fotakis, D.: A primal-dual algorithm for online non-uniform facility location. Journal of Discrete Algorithms 5, 141–148 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Fotakis, D.: On the competitive ratio for online facility location. Algorithmica (2007); Published online October 24, 2007. Previous version in ICALP 2003Google Scholar
  4. 4.
    Jain, K., Mahdian, M., Markakis, E., Saberi, A., Vazirani, V.: Greedy facility location algorithms analyzed using dual fitting with factor-revealing LP. Journal of the ACM 50, 795–824 (2003)CrossRefMathSciNetGoogle Scholar
  5. 5.
    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, 274–296 (2001)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Meyerson, A.: Online facility location. In: Proceedings of the 42nd Annual IEEE Symposium on Foundations of Computer Science, pp. 426–431 (2001)Google Scholar
  7. 7.
    Meyerson, A.: The parking permit problem. In: Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science, pp. 274–282 (2005)Google Scholar
  8. 8.
  9. 9.
    Swamy, C., Shmoys, D.B.: Sampling-based approximation algorithms for multi-stage stochastic optimization. In: Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science, pp. 357–366 (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Chandrashekhar Nagarajan
    • 1
  • David P. Williamson
    • 1
  1. 1.School of Operations Research and Information EngineeringCornell UniversityIthacaUSA

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