Graph Invariants as Necessary Conditions for Global Constraints

This article presents a database of about 200 graph invariants for deriving systematically necessary conditions from the graph properties based representation of global constraints. This scheme is based on invariants on the graph characteristics used in the description of a global constraint. A SICStus Prolog implementation based on arithmetic and logical constraints as well as on indexicals is available.

[1]  Nicolas Beldiceanu,et al.  Global Constraint Catalog , 2005 .

[2]  Toby Walsh,et al.  Extensions to Proof Planning for Generating Implied Constraints , 2001 .

[3]  Toby Walsh,et al.  Filtering Algorithms for the NValue Constraint , 2006, Constraints.

[4]  Mats Carlsson,et al.  Entailment of Finite Domain Constraints , 1994, ICLP.

[5]  Krzysztof R. Apt,et al.  Logic Programming , 1990, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[6]  Pascal Van Hentenryck,et al.  Solving the Car-Sequencing Problem in Constraint Logic Programming , 1988, ECAI.

[7]  Mats Carlsson,et al.  Deriving Filtering Algorithms from Constraint Checkers , 2004, CP.

[8]  Thierry Petit,et al.  Bornes de Caractéristiques de Graphes , 2005 .

[9]  Nicolas Beldiceanu,et al.  Introducing global constraints in CHIP , 1994 .

[10]  Xavier Lorca,et al.  The tree Constraint , 2005, CPAIOR.

[11]  Mark Wallace,et al.  Principles and Practice of Constraint Programming – CP 2004 , 2004, Lecture Notes in Computer Science.

[12]  Mats Carlsson,et al.  SICStus Prolog User''s Manual , 1993 .

[13]  Jean-Charles Régin,et al.  A Filtering Algorithm for Constraints of Difference in CSPs , 1994, AAAI.

[14]  Pascal Van Hentenryck,et al.  Constraint processing in cc(fd) , 1992 .

[15]  Toby Walsh,et al.  Principles and Practice of Constraint Programming — CP 2001: 7th International Conference, CP 2001 Paphos, Cyprus, November 26 – December 1, 2001 Proceedings , 2001, Lecture Notes in Computer Science.

[16]  Nicolas Beldiceanu.  Pruning for the Minimum Constraint Family and for the Number of Distinct Values Constraint Family , 2001, CP.

[17]  L. Moser,et al.  AN EXTREMAL PROBLEM IN GRAPH THEORY , 2001 .

[18]  Peter van Beek,et al.  Principles and Practice of Constraint Programming - CP 2005, 11th International Conference, CP 2005, Sitges, Spain, October 1-5, 2005, Proceedings , 2005, CP.

[19]  Nicolas Beldiceanu,et al.  Bounds of Graph Characteristics , 2005, CP.

[20]  P. Erdös.  On an extremal problem in graph theory , 1970 .

[21]  Toby Walsh,et al.  Filtering Algorithms for the NValue Constraint , 2005, CPAIOR.