Advertisement

Labelled (Hyper)Graphs, Negotiations and the Naming Problem

  • Jérémie Chalopin
  • Antoni Mazurkiewicz
  • Yves Métivier
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5214)

Abstract

We consider four different models of process interactions that unify and generalise models introduced and studied by Angluin et al. [2] and models introduced and studied by Mazurkiewicz [17,18]. We encode these models by labelled (hyper)graphs and relabelling rules on this labelled (hyper)graphs called negotiations. Then for these models, we give complete characterisations of labelled graphs in which the naming problem can be solved. Our characterizations are expressed in terms of locally constrained homomorphisms that are generalisations of known graph homomorphisms.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Angluin, D.: Local and global properties in networks of processors. In: Proceedings of the 12th Symposium on Theory of Computing, STOC 1980, pp. 82–93 (1980)Google Scholar
  2. 2.
    Angluin, D., Aspnes, J., Diamadi, Z., Fisher, M.J., Peralta, R.: Computation in networks of passively mobile finite-state sensors. In: Proc. of the 23th Symposium on Principles of Distributed Computing, pp. 290–299 (2004)Google Scholar
  3. 3.
    Angluin, D., Aspnes, J., Eisenstat, D.: Stably computable predicates are semilinear. In: Proc. of the 25th Symposium on Principles of Distributed Computing (2006)Google Scholar
  4. 4.
    Angluin, D., Aspnes, J., Eisenstat, D., Ruppert, E.: On the power of anonymous one-way communication. In: Proc. 9th conf. on Principles of Distributed Computing, pp. 307–318 (2005)Google Scholar
  5. 5.
    Boldi, P., Codenotti, B., Gemmell, P., Shammah, S., Simon, J., Vigna, S.: Symmetry breaking in anonymous networks: Characterizations. In: Proc. 4th Israeli Symposium on Theory of Computing and Systems, pp. 16–26. IEEE Press, Los Alamitos (1996)Google Scholar
  6. 6.
    Boldi, P., Vigna, S.: Fibrations of graphs. Discrete Math. 243, 21–66 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Boldi, P., Vigna, S.: An effective characterization of computability in anonymous networks. In: Welch, J.L. (ed.) DISC 2001. LNCS, vol. 2180, pp. 33–47. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  8. 8.
    Chalopin, J.: Election and local computations on closed unlabelled edges. In: Vojtáš, P., Bieliková, M., Charron-Bost, B., Sýkora, O. (eds.) SOFSEM 2005. LNCS, vol. 3381, pp. 81–90. Springer, Heidelberg (2005)Google Scholar
  9. 9.
    Chalopin, J., Métivier, Y.: Election and local computations on edges. In: Walukiewicz, I. (ed.) FOSSACS 2004. LNCS, vol. 2987, pp. 90–104. Springer, Heidelberg (2004)Google Scholar
  10. 10.
    Chalopin, J., Métivier, Y., Zielonka, W.: Election, naming and cellular edge local computations. In: Ehrig, H., Engels, G., Parisi-Presicce, F., Rozenberg, G. (eds.) ICGT 2004. LNCS, vol. 3256, pp. 242–256. Springer, Heidelberg (2004)Google Scholar
  11. 11.
    Chalopin, J., Métivier, Y., Zielonka, W.: Local computations in graphs: the case of cellular edge local computations. Fundamenta Informaticae 74(1), 85–114 (2006)zbMATHMathSciNetGoogle Scholar
  12. 12.
    Chalopin, J., Paulusma, D.: Graphs labelings derived from models in distributed computing (submitted)Google Scholar
  13. 13.
    Fiala, J., Paulusma, D.: A complete complexity classification of the role assignement problem. Theoretical computer science (to appear)Google Scholar
  14. 14.
    Godard, E., Métivier, Y., Muscholl, A.: Characterization of Classes of Graphs Recognizable by Local Computations. Theory of Computing Systems 37(2), 249–293 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Kratochvil, J., Proskurowski, A., Telle, J.A.: Complexity of graph covering problems. Nordic Journal of Computing 5, 173–195 (1998)zbMATHMathSciNetGoogle Scholar
  16. 16.
    Mazurkiewicz, A.: Distributed enumeration. Inf. Processing Letters 61(5), 233–239 (1997)CrossRefMathSciNetGoogle Scholar
  17. 17.
    Mazurkiewicz, A.: Bilateral ranking negotiations. Fundamenta Informaticae 60, 1–16 (2004)zbMATHMathSciNetGoogle Scholar
  18. 18.
    Mazurkiewicz, A.: Multilateral ranking negotiations. Fundamenta Informaticae 63, 241–258 (2004)zbMATHMathSciNetGoogle Scholar
  19. 19.
    Reidemeister, K.: Einführung in die Kombinatorische Topologie. Vieweg, Brunswick (1932)Google Scholar
  20. 20.
    Yamashita, M., Kameda, T.: Computing on anonymous networks: Part i - characterizing the solvable cases. IEEE Transactions on parallel and distributed systems 7(1), 69–89 (1996)CrossRefGoogle Scholar
  21. 21.
    Yamashita, M., Kameda, T.: Computing on anonymous networks: Part ii - decision and membership problems. IEEE Transactions on parallel and distributed systems 7(1), 90–96 (1996)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Jérémie Chalopin
    • 1
  • Antoni Mazurkiewicz
    • 2
  • Yves Métivier
    • 3
  1. 1.LIF, Aix-Marseille UniversitéMarseilleFrance
  2. 2.Institue of Computer Science of PASWarsawPoland
  3. 3.Université de Bordeaux, LaBRITalenceFrance

Personalised recommendations