Bounds of Graph Characteristics

This article presents a basic scheme for deriving systematically a filtering algorithm from the graph properties based representation of global constraints. This scheme is based on the bounds of the graph characteristics used in the description of a global constraint. The article provides bounds for the most common used graph characteristics.

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

[2]  Kurt Mehlhorn,et al.  Faster Algorithms for Bound-Consistency of the Sortedness and the Alldifferent Constraint , 2000, CP.

[3]  Jean-Charles Régin,et al.  Generalized Arc Consistency for Global Cardinality Constraint , 1996, AAAI/IAAI, Vol. 1.

[4]  Jean-Charles Régin The Symmetric Alldiff Constraint , 1999, IJCAI.

[5]  Peter van Beek,et al.  Improved Algorithms for the Global Cardinality Constraint , 2004, CP.

[6]  Willem Jan van Hoeve,et al.  A Hyper-arc Consistency Algorithm for the Soft Alldifferent Constraint , 2004, CP.

[7]  R. Z. Norman,et al.  An algorithm for a minimum cover of a graph , 1959 .

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

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

[10]  Dávid Hanák Implementing Global Constraints as Graphs of Elementary Constraints , 2003, Acta Cybern..

[11]  Christian Bessiere,et al.  Refining the Basic Constraint Propagation Algorithm , 2001, JFPLC.

[12]  Ugo Montanari,et al.  Networks of constraints: Fundamental properties and applications to picture processing , 1974, Inf. Sci..

[13]  Pascal Van Hentenryck,et al.  A Generic Arc-Consistency Algorithm and its Specializations , 1992, Artif. Intell..

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

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

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

[17]  Nageshwara Rao Vempaty Solving Constraint Satisfaction Problems Using Finite State Automata , 1992, AAAI.

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

[19]  Gilles Pesant,et al.  A Regular Language Membership Constraint for Finite Sequences of Variables , 2004, CP.

[20]  Pascal Van Hentenryck,et al.  Design, Implementation, and Evaluation of the Constraint Language cc(FD) , 1994, Constraint Programming.

[21]  Nicolas Beldiceanu,et al.  Global Constraints as Graph Properties on a Structured Network of Elementary Constraints of the Same Type , 2000, CP.

[22]  Irit Katriel,et al.  Fast Bound Consistency for the Global Cardinality Constraint , 2003, CP.

[23]  V. N. Rao,et al.  Solving constraint satisfaction problems using finite state automata , 1992, AAAI 1992.

[24]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .