Semiring-Based CSPs and Valued CSPs: Frameworks, Properties, and Comparison

In this paper we describe and compare two frameworks for constraint solving where classical CSPs, fuzzy CSPs, weighted CSPs, partial constraint satisfaction, and others can be easily cast. One is based on a semiring, and the other one on a totally ordered commutative monoid. While comparing the two approaches, we show how to pass from one to the other one, and we discuss when this is possible. The two frameworks have been independently introduced in ijcai95,jacm and schiex-ijcai95.

[1]  Thomas Schiex,et al.  Possibilistic Constraint Satisfaction Problems or "How to Handle Soft Constraints?" , 1992, UAI.

[2]  Thomas Schiex,et al.  Valued Constraint Satisfaction Problems: Hard and Easy Problems , 1995, IJCAI.

[3]  Prakash P. Shenoy.  Valuation-based systems for discrete optimisation , 1990, UAI.

[4]  Eugene C. Freuder.  Backtrack-free and backtrack-bounded search , 1988 .

[5]  Thomas Schiex,et al.  Maintaining Reversible DAC for Max-CSP , 1999, Artif. Intell..

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

[7]  Yan Georget,et al.  Compiling Semiring-Based Constraints with clp (FD, S) , 1998, CP.

[8]  Eugene C. Freuder,et al.  Partial Constraint Satisfaction , 1989, IJCAI.

[9]  Eugene C. Freuder,et al.  An Efficient Cross Product Representation of the Constraint Satisfaction Problem Search Space , 1992, AAAI.

[10]  Francesca Rossi,et al.  Constraint Relaxation may be Perfect , 1991, Artif. Intell..

[11]  Robert M. Haralick,et al.  Structural Descriptions and Inexact Matching , 1981, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[12]  Thomas Schiex,et al.  Russian Doll Search for Solving Constraint Optimization Problems , 1996, AAAI/IAAI, Vol. 1.

[13]  Jérôme Lang,et al.  Uncertainty in Constraint Satisfaction Problems: a Probalistic Approach , 1993, ECSQARU.

[14]  Francesca Rossi,et al.  Semiring-based Constraint Logic Programming , 1997, IJCAI.

[15]  Didier Dubois,et al.  A class of fuzzy measures based on triangular norms , 1982 .

[16]  Z. Ruttkay.  Fuzzy constraint satisfaction , 1994, Proceedings of 1994 IEEE 3rd International Fuzzy Systems Conference.

[17]  Prakash P. Shenoy,et al.  Valuation-based systems: a framework for managing uncertainty in expert systems , 1992 .

[18]  Alan K. Mackworth.  Consistency in Networks of Relations , 1977, Artif. Intell..

[19]  Francesca Rossi,et al.  Constraint Solving over Semirings , 1995, IJCAI.

[20]  Javier Larrosa,et al.  Exploiting the Use of DAC in MAX-CSP , 1996, CP.

[21]  Eugene C. Freuder,et al.  Improved relaxation and search methods for approximate constraint satisfaction with a maximin criter , 1990 .

[22]  Francesca Rossi,et al.  Semiring-based constraint satisfaction and optimization , 1997, JACM.

[23]  Michael J. Maher,et al.  Constraint Hierarchies and Logic Programming , 1989, ICLP.

[24]  Eugene C. Freuder.  Synthesizing constraint expressions , 1978, CACM.

[25]  Thomas Schiex,et al.  Selecting preferred solutions in Fuzzy Constraint Satisfaction Problems , 1993 .

[26]  Vipin Kumar,et al.  Algorithms for Constraint-Satisfaction Problems: A Survey , 1992, AI Mag..

[27]  H. Moulin.  Axioms of Cooperative Decision Making , 1988 .

[28]  Bernard A. Nadel,et al.  Constraint satisfaction algorithms 1 , 1989, Comput. Intell..

[29]  Joxan Jaffar,et al.  Constraint logic programming , 1987, POPL '87.

[30]  Thomas Schiex,et al.  Reversible DAC and Other Improvements for Solving Max-CSP , 1998, AAAI/IAAI.

[31]  L. Zadeh.  Calculus of fuzzy restrictions , 1996 .

[32]  Francesca Rossi,et al.  Semiring-based constraint solving and optimization , 1997 .

[33]  Mark W. Krentel.  The Complexity of Optimization Problems , 1986, Computational Complexity Conference.

[34]  D. Dubois,et al.  The calculus of fuzzy restrictions as a basis for flexible constraint satisfaction , 1993, [Proceedings 1993] Second IEEE International Conference on Fuzzy Systems.

[35]  David S. Johnson,et al.  Some Simplified NP-Complete Graph Problems , 1976, Theor. Comput. Sci..

[36]  Eugene C. Freuder,et al.  The Complexity of Some Polynomial Network Consistency Algorithms for Constraint Satisfaction Problems , 1985, Artif. Intell..

[37]  Simon de Givry,et al.  Bounding the Optimum of Constraint Optimization Problems , 1997, CP.

[38]  Jf Baldwin,et al.  Encyclopedia of AI , 1992 .