Effect of DisCSP Variable-Ordering Heuristics in Scale-Free Networks

  • Tenda Okimoto
  • Atsushi Iwasaki
  • Makoto Yokoo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7057)


A Distributed Constraint Satisfaction Problem (DisCSP) is a constraint satisfaction problem in which variables and constraints are distributed among multiple agents. Various algorithms for solving DisCSPs have been developed, which are intended for general purposes, i.e., they can be applied to any network structure. However, if a network has some particular structure, e.g., the network structure is scale-free, we can expect that some specialized algorithms or heuristics, which are tuned for the network structure, can outperform general purpose algorithms/heuristics.

In this paper, as an initial step toward developing specialized algorithms for particular network structures, we examine variable-ordering heuristics in scale-free networks. We use the classic asynchronous backtracking algorithm as a baseline algorithm and examine the effect of variable-ordering heuristics. First, we show that the choice of variable-ordering heuristics is more influential in scale-free networks than in random networks. Furthermore, we develop a novel variable-ordering heuristic that is specialized to scale-free networks. Experimental results illustrate that our new variable-ordering heuristic is more effective than a standard degree-based variable-ordering heuristic. Our proposed heuristic reduces the required cycles by 30% at the critical point.


Random Graph Degree Distribution Random Network Constraint Satisfaction Problem Constraint Tightness 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Yokoo, M., Durfee, E.H., Ishida, T., Kuwabara, K.: The distributed constraint satisfaction problem: formalization and algorithms. IEEE Transactions on Knowledge and Data Engineering 10(5), 673–685 (1998)CrossRefGoogle Scholar
  2. 2.
    Yokoo, M., Hirayama, K.: Algorithms for distributed constraint satisfaction: A review. Journal of Autonomous Agents and Multi-agent Systems 3(2), 189–211 (2000)CrossRefGoogle Scholar
  3. 3.
    Hamadi, Y.: Backtracking in distributed constraint networks. International Journal on Artificial Intelligence Tools, 219–223 (1998)Google Scholar
  4. 4.
    Bessiere, C., Brito, I., Maestre, A., Meseguer, P.: Asynchronous backtracking without adding links: a new member in the ABT family. Artificial Intelligence 161, 7–24 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Nguyen, V., Sam-Haroud, D., Faltings, B.: Dynamic distributed backjumping. In: Joint ERCIM/CoLogNet International Workshop on Constraint Solving and Constraint Logic Programming, pp. 71–85 (2004)Google Scholar
  6. 6.
    Mailler, R., Lesser, V.: Asynchronous partial overlay: A new algorithm for solving distributed constraint satisfaction problems. Journal of Artificial Intelligence Research 25, 529–576 (2006)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Silaghi, M.-C.: Framework for modeling reordering heuristics for asynchronous backtracking. In: IEEE/WIC/ACM International Conference on intelligent Agent Technology, pp. 529–536 (2006)Google Scholar
  8. 8.
    Zivan, R., Meisels, A.: Dynamic ordering for asynchronous backtracking on DisCSPs. Constraints 11(2-3), 179–197 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Erdös, P., Rényi, A.: On random graphs I. Publicationes Mathematicae Debrecen 6, 290–297 (1959)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Barabási, A.-L.: Linked: The new science of networks. Perseus Publishing, Cambridge (2003)Google Scholar
  11. 11.
    Barabási, A.-L., Albert, R.: Emergence of scaling in random networks. Science 286, 509–512 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Devlin, D., O’Sullivan, B.: Preferential attachment in constraint networks. In: 21st International Conference on Tools with Artificial Intelligence, pp. 708–715 (2009)Google Scholar
  13. 13.
    Walsh, T.: Search in a small world. In: 16th International Joint Conference on Artificial Intelligence, pp. 1172–1177 (1999)Google Scholar
  14. 14.
    Walsh, T.: Search on high degree graphs. In: 17th International Joint Conference on Artificial Intelligence, pp. 266–274 (2001)Google Scholar
  15. 15.
    Chalupsky, H., Gil, Y., Knoblock, C.A., Lerman, K., Oh, J., Pynadath, D.V., Russ, T.A., Tambe, M.: Electric elves: Agent technology for supporting human organizations. AI Magazine 23(2), 11–24 (2002)Google Scholar
  16. 16.
    Brito, I., Meseguer, P.: Distributed meeting scheduling. In: Computer & Communications Industry Association, pp. 38–45 (2007)Google Scholar
  17. 17.
    Arbelaez, A., Hamadi, Y.: Exploiting weak dependencies in tree-based search. In: 24th Annual ACM Symposium on Applied Computing, pp. 1385–1391 (2009)Google Scholar
  18. 18.
    Ezzahir, R., Bessiere, C., Wahbi, M., Benelallam, I., Bouyakhf, E.H.: Asynchronous Inter-Level Forward-Checking for DisCSPs. In: Gent, I.P. (ed.) CP 2009. LNCS, vol. 5732, pp. 304–318. Springer, Heidelberg (2009)Google Scholar
  19. 19.
    Hamadi, Y.: Interleaved backtracking in distributed constraint networks. International Journal on Artificial Intelligence Tools 11(2), 167–188 (2002)CrossRefGoogle Scholar
  20. 20.
    Sultanik, E., Lass, R.N., Regli, W.C.: Dynamic configuration of agent organizations. In: 21st International Joint Conference on Artificial Intelligence, pp. 305–311 (2009)Google Scholar
  21. 21.
    Mackworth, A.K.: Constraint Satisfaction. In: Encyclopedia of Artificial Intelligence, pp. 285–293 (1992)Google Scholar
  22. 22.
    Buchanan, M.: Nexus: Small worlds and the groundbreaking science of networks. W. W. Norton & Company, London (2003)Google Scholar
  23. 23.
    Li, L., Alderson, D., Doyle, J.C., Willinger, W.: Towards a theory of scale-free graphs: Definition, properties, and implications. Internet Mathematics 2(4), 431–523 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Densmore, O.: An exploration of power-law networks (2009),

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Tenda Okimoto
    • 1
  • Atsushi Iwasaki
    • 1
  • Makoto Yokoo
    • 1
  1. 1.Kyushu UniversityFukuokaJapan

Personalised recommendations