, Volume 22, Issue 2, pp 230–264 | Cite as

Triangle-based consistencies for cost function networks

  • Hiep Nguyen
  • Christian Bessiere
  • Simon de Givry
  • Thomas SchiexEmail author


Cost Function Networks (aka Weighted CSP) allow to model a variety of problems, such as optimization of deterministic and stochastic graphical models including Markov random Fields and Bayesian Networks. Solving cost function networks is thus an important problem for deterministic and probabilistic reasoning. This paper focuses on local consistencies which define essential tools to simplify Cost Function Networks, and provide lower bounds on their optimal solution cost. To strengthen arc consistency bounds, we follow the idea of triangle-based domain consistencies for hard constraint networks (path inverse consistency, restricted or max-restricted path consistencies), describe their systematic extension to cost function networks, study their relative strengths, define enforcing algorithms, and experiment with them on a large set of benchmark problems. On some of these problems, our improved lower bounds seem necessary to solve them.


Cost function networks Weighted CSP Constraint optimization problems High order consistencies Restricted path consistency Path inverse consistency Max-restricted path consistency 



This work has been partly funded by the “Agence nationale de la Recherche”, reference ANR-10-BLA-0214


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.MIAT, UR 875Université de Toulouse, INRACastanet-TolosanFrance
  2. 2.University of MontpellierMontpellierFrance

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