Tradeoffs in Process Strategy Games with Application in the WDM Reconfiguration Problem

  • Nathann Cohen
  • David Coudert
  • Dorian Mazauric
  • Napoleão Nepomuceno
  • Nicolas Nisse
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6099)


We consider a variant of the graph searching games that is closely related to the routing reconfiguration problem in WDM networks. In the digraph processing game, a team of agents is aiming at clearing, or processing, the vertices of a digraph D. In this game, two important measures arise: 1) the total number of agents used, and 2) the total number of vertices occupied by an agent during the processing of D. Previous works have studied the problem of minimizing each of these parameters independently. In particular, both of these optimization problems are not in APX. In this paper, we study the tradeoff between both these conflicting objectives. More precisely, we prove that there exist some instances for which minimizing one of these objectives arbitrarily impairs the quality of the solution for the other one. We show that such bad tradeoffs may happen even in the case of basic network topologies. On the other hand, we exhibit classes of instances where good tradeoffs can be achieved. We also show that minimizing one of these parameters while the other is constrained is not in APX.


Graph searching process number routing reconfiguration 


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  1. 1.
    Breisch, R.L.: An intuitive approach to speleotopology. Southwestern Cavers VI(5), 72–78 (1967)Google Scholar
  2. 2.
    Cohen, N., Coudert, D., Mazauric, D., Nepomuceno, N., Nisse, N.: Tradeoffs when optimizing lightpaths reconfiguration in WDM networks. RR 7047, INRIA (2009)Google Scholar
  3. 3.
    Coudert, D., Huc, F., Mazauric, D.: A distributed algorithm for computing and updating the process number of a forest. In: Taubenfeld, G. (ed.) DISC 2008. LNCS, vol. 5218, pp. 500–501. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  4. 4.
    Coudert, D., Huc, F., Mazauric, D., Nisse, N., Sereni, J.-S.: Routing reconfiguration/process number: Coping with two classes of services. In: 13th Conf. on Optical Network Design and Modeling, ONDM (2009)Google Scholar
  5. 5.
    Coudert, D., Perennes, S., Pham, Q.-C., Sereni, J.-S.: Rerouting requests in wdm networks. In: AlgoTel 2005, May 2005, pp. 17–20 (2005)Google Scholar
  6. 6.
    Coudert, D., Sereni, J.-S.: Characterization of graphs and digraphs with small process number. Research Report 6285, INRIA (September 2007)Google Scholar
  7. 7.
    Deo, N., Krishnamoorthy, S., Langston, M.A.: Exact and approximate solutions for the gate matrix layout problem. IEEE Tr. on Comp.-Aided Design 6, 79–84 (1987)CrossRefGoogle Scholar
  8. 8.
    Ellis, J.A., Sudborough, I.H., Turner, J.S.: The vertex separation and search number of a graph. Information and Computation 113(1), 50–79 (1994)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Fomin, F., Thilikos, D.: An annotated bibliography on guaranteed graph searching. Theo. Comp. Sci. 399(3), 236–245 (2008)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, New York (1979)MATHGoogle Scholar
  11. 11.
    Jose, N., Somani, A.K.: Connection rerouting/network reconfiguration. In: Design of Reliable Communication Networks. IEEE, Los Alamitos (2003)Google Scholar
  12. 12.
    Kirousis, M., Papadimitriou, C.H.: Searching and pebbling. Theoretical Comp. Sc. 47(2), 205–218 (1986)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Megiddo, N., Hakimi, S.L., Garey, M.R., Johnson, D.S., Papadimitriou, C.H.: The complexity of searching a graph. J. Assoc. Comput. Mach. 35(1), 18–44 (1988)MATHMathSciNetGoogle Scholar
  14. 14.
    Parsons, T.D.: Pursuit-evasion in a graph. In: Theory and applications of graphs. Lecture Notes in Mathematics, vol. 642, pp. 426–441. Springer, Berlin (1978)CrossRefGoogle Scholar
  15. 15.
    Robertson, N., Seymour, P.D.: Graph minors. I. Excluding a forest. J. Comb. Th. Ser. B 35(1), 39–61 (1983)MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Solano, F.: Analyzing two different objectives of the WDM network reconfiguration problem. In: IEEE Global Communications Conference, Globecom (2009)Google Scholar
  17. 17.
    Solano, F., Pióro, M.: A mixed-integer programing formulation for the lightpath reconfiguration problem. In: VIII Workshop on G/MPLS Networks, WGN8 (2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Nathann Cohen
    • 1
  • David Coudert
    • 1
  • Dorian Mazauric
    • 1
  • Napoleão Nepomuceno
    • 1
    • 2
  • Nicolas Nisse
    • 1
  1. 1.MASCOTTE, INRIA, I3S, CNRS, UNSSophia AntipolisFrance
  2. 2.Universidade Federal do Ceará, Fortaleza-CEBrazil

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