Advertisement

Strategic Online Facility Location

  • Maximilian Drees
  • Björn FeldkordEmail author
  • Alexander Skopalik
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10043)

Abstract

In this paper we consider a strategic variant of the online facility location problem. Given is a graph in which each node serves two roles: it is a strategic client stating requests as well as a potential location for a facility. In each time step one client states a request which induces private costs equal to the distance to the closest facility. Before serving, the clients may collectively decide to open new facilities, sharing the corresponding price. Instead of optimizing the global costs, each client acts selfishly. The prices of new facilities vary between nodes and also change over time, but are always bounded by some fixed value \(\alpha \). Both the requests as well as the facility prices are given by an online sequence and are not known in advance.

We characterize the optimal strategies of the clients and analyze their overall performance in comparison to a centralized offline solution. If all players optimize their own competitiveness, the global performance of the system is \(\mathcal {O}(\sqrt{\alpha }\cdot \alpha )\) times worse than the offline optimum. A restriction to a natural subclass of strategies improves this result to \(\mathcal {O}(\alpha )\). We also show that for fixed facility costs, we can find strategies such that this bound further improves to \(\mathcal {O}(\sqrt{\alpha })\).

Keywords

Online algorithms Competitive analysis Facility location Algorithmic game theory 

References

  1. 1.
    Albers, S., Koga, H.: New on-line algorithms for the page replication problem. J. Algorithms 27(1), 75–96 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Awerbuch, B., Bartal, Y., Fiat, A.: Competitive distributed file allocation. In: Proceedings of the 25th Annual ACM Symposium on Theory of Computing (STOC), pp. 164–173. ACM (1993)Google Scholar
  3. 3.
    Bienkowski, M.: Price fluctuations: to buy or to rent. In: Bampis, E., Jansen, K. (eds.) WAOA 2009. LNCS, vol. 5893, pp. 25–36. Springer, Heidelberg (2010). doi: 10.1007/978-3-642-12450-1_3 CrossRefGoogle Scholar
  4. 4.
    Fotakis, D.: On the competitive ratio for online facility location. Algorithmica 50(1), 1–57 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Fotakis, D., Tzamos, C.: On the power of deterministic mechanisms for facility location games. ACM Trans. Econ. Comput. 2(4), 15:1–15:37 (2014)CrossRefzbMATHGoogle Scholar
  6. 6.
    Immorlica, N., Kalai, A.T., Lucier, B., Moitra, A., Postlewaite, A., Tennenholtz, M.: Dueling algorithms. In: Proceedings of the 43rd Annual ACM Symposium on Theory of Computing (STOC), pp. 215–224. ACM (2011)Google Scholar
  7. 7.
    Kling, P., auf der Heide, F.M., Pietrzyk, P.: An algorithm for online facility leasing. In: Even, G., Halldórsson, M.M. (eds.) SIROCCO 2012. LNCS, vol. 7355, pp. 61–72. Springer, Heidelberg (2012). doi: 10.1007/978-3-642-31104-8_6 CrossRefGoogle Scholar
  8. 8.
    Meyerson, A.: Online facility location. In: Proceedings of the 42nd IEEE Symposium on Foundations of Computer Science (FOCS), pp. 426–431 (2001)Google Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Maximilian Drees
    • 1
  • Björn Feldkord
    • 1
    Email author
  • Alexander Skopalik
    • 1
  1. 1.Heinz Nixdorf InstitutePaderborn UniversityPaderbornGermany

Personalised recommendations