Predicting Phase Transitions of Binary Constraint Satisfaction Problems with Constraint Graph Information

Constraint satisfaction is at the core of many applications, such as scheduling. The study of phase transition has benefited algorithm selection and algorithm development in constraint satisfaction. Recent research provides evidence that constraint graph topology affects where phase transitions occur in constraint satisfaction problems. In this article, a new phase transition predictor which takes constraint graph information into consideration is proposed. The new predictor allows variation in the tightness of individual constraints and node degree variation in constraint graph. Experiments were conducted to study the usefulness of the new predictor on random binary constraint satisfaction problems. Results show that the new predictor is able to produce predictions as good as the state-of-the-art predictor in general, but do considerably better in sparsely constrained problems, particularly when the node degree variation in their constraint graphs is high.

[1]  Patrick Prosser,et al.  An Empirical Study of Phase Transitions in Binary Constraint Satisfaction Problems , 1996, Artif. Intell..

[2]  Peter van Beek,et al.  A theoretical evaluation of selected backtracking algorithms , 1995, IJCAI 1995.

[3]  Tad Hogg,et al.  Refining the Phase Transition in Combinatorial Search , 1996, Artif. Intell..

[4]  Jean-francois Puget,et al.  A C++ implementation of CLP , 1997 .

[5]  Romulus Dan Vlasie.  Systematic generation of very hard cases for graph 3-colorability , 1995, Proceedings of 7th IEEE International Conference on Tools with Artificial Intelligence.

[6]  Pascal Van Hentenryck,et al.  The Constraint Logic Programming Language CHIP , 1988, FGCS.

[7]  Peter C. Cheeseman,et al.  Where the Really Hard Problems Are , 1991, IJCAI.

[8]  Daniel Brélaz,et al.  New methods to color the vertices of a graph , 1979, CACM.

[9]  Robert E. Mercer,et al.  A New Model of Hard Binary Constraint Satisfaction Problems , 1996, Canadian Conference on AI.

[10]  Toby Walsh,et al.  The Scaling of Search Cost , 1997, AAAI/IAAI.

[11]  Edward P. K. Tsang,et al.  Foundations of constraint satisfaction , 1993, Computation in cognitive science.

[12]  Christian Bessiere,et al.  MAC and Combined Heuristics: Two Reasons to Forsake FC (and CBJ?) on Hard Problems , 1996, CP.

[13]  James M. Crawford,et al.  Experimental Results on the Crossover Point inSatis ability , 1993 .

[14]  Toby Walsh,et al.  Phase Transitions and Annealed Theories: Number Partitioning as a Case Study , 1996, ECAI.

[15]  Alain Colmerauer,et al.  An introduction to Prolog III , 1989, CACM.

[16]  Patrick Prosser,et al.  Forward Checking with Backmarking , 1995, Constraint Processing, Selected Papers.

[17]  Eugene C. Freuder,et al.  Contradicting Conventional Wisdom in Constraint Satisfaction , 1994, ECAI.

[18]  Hector J. Levesque,et al.  Hard and Easy Distributions of SAT Problems , 1992, AAAI.

[19]  Barbara M. Smith,et al.  The Phase Transition and the Mushy Region in Constraint Satisfaction Problems , 1994, ECAI.

[20]  Edward P. K. Tsang,et al.  Adaptive Constraint Satisfaction: The Quickest First Principle , 1996, ECAI.

[21]  Toby Walsh,et al.  The Constrainedness of Search , 1996, AAAI/IAAI, Vol. 1.

[22]  Robert M. Haralick,et al.  Increasing Tree Search Efficiency for Constraint Satisfaction Problems , 1979, Artif. Intell..

[23]  Martin E. Dyer,et al.  Locating the Phase Transition in Binary Constraint Satisfaction Problems , 1996, Artif. Intell..

[24]  Toby Walsh,et al.  The SAT Phase Transition , 1994, ECAI.

[25]  Mark Wallace,et al.  Constraint logic programming for scheduling and planning , 1995 .

[26]  Tad Hogg,et al.  Exploiting the Deep Structure of Constraint Problems , 1994, Artif. Intell..

[27]  David Robertson,et al.  Proceedings of the 12th European Conference on Artificial Intelligence , 1996 .

[28]  Toby Walsh,et al.  Phase Transitions from Real Computational Problems , 1995 .

[29]  Patrick Prosser,et al.  HYBRID ALGORITHMS FOR THE CONSTRAINT SATISFACTION PROBLEM , 1993, Comput. Intell..

[30]  Tad Hogg,et al.  Phase Transitions and the Search Problem , 1996, Artif. Intell..