On a Non-cooperative Model for Wavelength Assignment in Multifiber Optical Networks

  • Evangelos Bampas
  • Aris Pagourtzis
  • George Pierrakos
  • Katerina Potika
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5369)

Abstract

We study path multicoloring games that describe situations in which selfish entities possess communication requests in a multifiber all-optical network. Each player is charged according to the maximum fiber multiplicity that her color (wavelength) choice incurs and the social cost is the maximum player cost. We investigate the price of anarchy of such games and provide two different upper bounds for general graphs—namely the number of wavelengths and the minimum length of a path of maximum disutility, over all worst-case Nash Equilibria—as well as matching lower bounds which hold even for trees; as a corollary we obtain that the price of anarchy in stars is exactly 2. We also prove constant bounds for the price of anarchy in chains and rings in which the number of wavelengths is relatively small compared to the load of the network; in the opposite case we show that the price of anarchy is unbounded.

Keywords

Selfish wavelength assignment non-cooperative games price of anarchy multifiber optical networks path multicoloring 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Andrews, M., Zhang, L.: Minimizing maximum fiber requirement in optical networks. J. Comput. Syst. Sci. 72(1), 118–131 (2006)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Andrews, M., Zhang, L.: Complexity of wavelength assignment in optical network optimization. In: INFOCOM 2006. IEEE, Los Alamitos (2006)Google Scholar
  3. 3.
    Andrews, M., Zhang, L.: Wavelength assignment in optical networks with fixed fiber capacity. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 134–145. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  4. 4.
    Nomikos, C., Pagourtzis, A., Zachos, S.: Routing and path multicoloring. Inf. Process. Lett. 80(5), 249–256 (2001)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Erlebach, T., Pagourtzis, A., Potika, K., Stefanakos, S.: Resource allocation problems in multifiber WDM tree networks. In: Bodlaender, H.L. (ed.) WG 2003. LNCS, vol. 2880, pp. 218–229. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  6. 6.
    Winkler, P., Zhang, L.: Wavelength assignment and generalized interval graph coloring. In: SODA, pp. 830–831 (2003)Google Scholar
  7. 7.
    Margara, L., Simon, J.: Wavelength assignment problem on all-optical networks with k fibres per link. In: Welzl, E., Montanari, U., Rolim, J.D.P. (eds.) ICALP 2000. LNCS, vol. 1853, pp. 768–779. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  8. 8.
    Li, G., Simha, R.: On the wavelength assignment problem in multifiber WDM star and ring networks. IEEE/ACM Trans. Netw. 9(1), 60–68 (2001)CrossRefGoogle Scholar
  9. 9.
    Nash, J.: Non-cooperative games. The Annals of Mathematics 54(2), 286–295 (1951)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Fotakis, D., Kontogiannis, S.C., Koutsoupias, E., Mavronicolas, M., Spirakis, P.G.: The structure and complexity of Nash equilibria for a selfish routing game. In: Widmayer, P., Triguero, F., Morales, R., Hennessy, M., Eidenbenz, S., Conejo, R. (eds.) ICALP 2002. LNCS, vol. 2380, pp. 123–134. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  11. 11.
    Rosenthal, R.W.: A class of games possessing pure-strategy Nash equilibria. Int. J. Game Theory 2, 65–67 (1973)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Milchtaich, I.: Congestion games with player-specific payoff functions. Games and Economic Behavior 13, 111–124 (1996)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Monderer, D., Shapley, L.S.: Potential games. Games and Economic Behavior 14, 124–143 (1996)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Koutsoupias, E., Papadimitriou, C.H.: Worst-case equilibria. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563, pp. 404–413. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  15. 15.
    Mavronicolas, M., Spirakis, P.G.: The price of selfish routing. In: STOC, pp. 510–519 (2001)Google Scholar
  16. 16.
    Roughgarden, T., Tardos, É.: How bad is selfish routing? J. ACM 49(2), 236–259 (2002)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Anshelevich, E., Dasgupta, A., Kleinberg, J.M., Tardos, É., Wexler, T., Roughgarden, T.: The price of stability for network design with fair cost allocation. In: FOCS, pp. 295–304. IEEE Computer Society, Los Alamitos (2004)Google Scholar
  18. 18.
    Busch, C., Magdon-Ismail, M.: Atomic routing games on maximum congestion. In: Cheng, S.-W., Poon, C.K. (eds.) AAIM 2006. LNCS, vol. 4041, pp. 79–91. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  19. 19.
    Banner, R., Orda, A.: Bottleneck routing games in communication networks. In: INFOCOM 2006. IEEE, Los Alamitos (2006)Google Scholar
  20. 20.
    Caragiannis, I., Galdi, C., Kaklamanis, C.: Network load games. In: Deng, X., Du, D.-Z. (eds.) ISAAC 2005. LNCS, vol. 3827, pp. 809–818. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  21. 21.
    Bilò, V., Moscardelli, L.: The price of anarchy in all-optical networks. In: Kralovic, R., Sýkora, O. (eds.) SIROCCO 2004. LNCS, vol. 3104, pp. 13–22. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  22. 22.
    Bilò, V., Flammini, M., Moscardelli, L.: On Nash equilibria in non-cooperative all-optical networks. In: Diekert, V., Durand, B. (eds.) STACS 2005. LNCS, vol. 3404, pp. 448–459. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  23. 23.
    Georgakopoulos, G.F., Kavvadias, D.J., Sioutis, L.G.: Nash equilibria in all-optical networks. In: Deng, X., Ye, Y. (eds.) WINE 2005. LNCS, vol. 3828, pp. 1033–1045. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  24. 24.
    Milis, I., Pagourtzis, A., Potika, K.: Selfish routing and path coloring in all-optical networks. In: Janssen, J., Prałat, P. (eds.) CAAN 2007. LNCS, vol. 4852, pp. 71–84. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  25. 25.
    Chien, S., Sinclair, A.: Convergence to approximate Nash equilibria in congestion games. In: SODA, pp. 169–178. SIAM, Philadelphia (2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Evangelos Bampas
    • 1
  • Aris Pagourtzis
    • 1
  • George Pierrakos
    • 1
  • Katerina Potika
    • 1
  1. 1.School of Elec. & Comp. Eng.National Technical University of Athens Polytechnioupoli ZografouAthensGreece

Personalised recommendations