Min-Max Message Passing and Local Consistency in Constraint Networks

  • Hong XuEmail author
  • T. K. Satish Kumar
  • Sven Koenig
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10400)


In this paper, we uncover some relationships between local consistency in constraint networks and message passing akin to belief propagation in probabilistic reasoning. We develop a new message passing algorithm, called the min-max message passing (MMMP) algorithm, for unifying the different notions of local consistency in constraint networks. In particular, we study its connection to arc consistency (AC) and path consistency. We show that AC-3 can be expressed more intuitively in the framework of message passing. We also show that the MMMP algorithm can be modified to enforce path consistency.


Message passing Constraint network Local consistency 


  1. 1.
    van Beek, P., Dechter, R.: On the minimality and global consistency of row-convex constraint networks. J. ACM 42(3), 543–561 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Freuder, E.C.: A sufficient condition for backtrack-free search. J. ACM 29(1), 24–32 (1982)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Jeavons, P.G., Cooper, M.C.: Tractable constraints on ordered domains. Artif. Intell. 79(2), 327–339 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Mackworth, A.K.: Consistency in networks of relations. Artif. Intell. 8(1), 99–118 (1977)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Mézard, M., Montanari, A.: Information, Physics, and Computation. Oxford University Press, Oxford (2009)CrossRefzbMATHGoogle Scholar
  6. 6.
    Mézard, M., Zecchina, R.: Random \(k\)-satisfiability problem: From an analytic solution to an efficient algorithm. Phys. Rev. E 66(5), 056126 (2002). doi: 10.1103/PhysRevE.66.056126 CrossRefGoogle Scholar
  7. 7.
    Russell, S., Norvig, P.: Artificial Intelligence: A Modern Approach, 3rd edn. Pearson, Upper Saddle River (2009)zbMATHGoogle Scholar
  8. 8.
    Xu, H., Satish Kumar, T.K., Koenig, S.: The Nemhauser-Trotter reduction and lifted message passing for the weighted CSP. In: Salvagnin, D., Lombardi, M. (eds.) CPAIOR 2017. LNCS, vol. 10335, pp. 387–402. Springer, Cham (2017). doi: 10.1007/978-3-319-59776-8_31 CrossRefGoogle Scholar
  9. 9.
    Yedidia, J.S., Freeman, W.T., Weiss, Y.: Bethe free energy, Kikuchi approximations, and belief propagation algorithms. Technical report R2001-16, Mitsubishi Electric Research Laboratories (2001)Google Scholar
  10. 10.
    Yedidia, J.S., Freeman, W.T., Weiss, Y.: Understanding belief propagation and its generalizations. Explor. Artif. Intell. New Millenn. 8, 239–269 (2003)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.University of Southern CaliforniaLos AngelesUSA

Personalised recommendations