Constraint Propagation

Publisher Summary This chapter discusses that constraint reasoning involves various types of techniques to tackle the inherent intractability of the problem of satisfying a set of constraints. Constraint propagation is one of those types of techniques. It is central to the process of solving a constraint problem and indispensable for constraint reasoning. The chapter examines that constraint propagation embeds any reasoning, which consists in explicitly forbidding values or combinations of values for some variables of a problem, because a given subset of its constraints cannot be satisfied otherwise. It is in constraint reasoning that this concept shows its most accomplished form. There is no other field in which the concept of constraint propagation appears in such a variety of forms, and in which its characteristics have been analyzed. The chapter reviews that it formalizes all constraint propagation approaches within a unifying framework and discusses the main existing types of constraint propagation.

[1]  Bernard A. Nadel,et al.  Tree search and ARC consistency in constraint satisfaction algorithms , 1988 .

[2]  Roman Barták,et al.  A General Relation Constraint: An Implementation , 2000 .

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

[4]  Marco Cadoli,et al.  A Survey on Knowledge Compilation , 1997, AI Commun..

[5]  Hervé Cros Compilation et apprentissage dans les réseaux de contraintes , 2003 .

[6]  Toby Walsh,et al.  The Constrainedness of Arc Consistency , 1997, CP.

[7]  Thom W. Frühwirth,et al.  Theory and Practice of Constraint Handling Rules , 1998, J. Log. Program..

[8]  Eugene C. Freuder,et al.  Neighborhood Inverse Consistency Preprocessing , 1996, AAAI/IAAI, Vol. 1.

[9]  David B. Shmoys,et al.  A New Approach to Computing Optimal Schedules for the Job-Shop Scheduling Problem , 1996, IPCO.

[10]  Toby Walsh,et al.  Singleton Consistencies , 2000, CP.

[11]  Frédéric Benhamou,et al.  Applying Interval Arithmetic to Real, Integer, and Boolean Constraints , 1997, J. Log. Program..

[12]  Roger Mohr,et al.  Good Old Discrete Relaxation , 1988, ECAI.

[13]  Philippe Jégou Contribution à l'étude des problèmes de satisfaction de contraintes : algorithmes de propagation et de résolution : propagation de contraintes dans les réseaux dynamiques , 1991 .

[14]  Peter J. Stuckey,et al.  Finite Domain Bounds Consistency Revisited , 2004, Australian Conference on Artificial Intelligence.

[15]  Christian Bessiere,et al.  Some Practicable Filtering Techniques for the Constraint Satisfaction Problem , 1997, IJCAI.

[16]  Philippe Jégou,et al.  Efficient Path-Consistency Propagation , 1998, Int. J. Artif. Intell. Tools.

[17]  Eugene C. Freuder A Sufficient Condition for Backtrack-Free Search , 1982, JACM.

[18]  Peter J. Stuckey,et al.  Box Constraint Collections for Adhoc Constraints , 2003, CP.

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

[20]  Christian Bessiere,et al.  From Restricted Path Consistency to Max-Restricted Path Consistency , 1997, CP.

[21]  Peter J. Stuckey,et al.  Speeding Up Constraint Propagation , 2004, CP.

[22]  Philippe Jégou,et al.  Path-Consistency: When Space Misses Time , 1996, AAAI/IAAI, Vol. 1.

[23]  Christophe Lecoutre,et al.  A Greedy Approach to Establish Singleton Arc Consistency , 2005, IJCAI.

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

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

[26]  Solomon W. Golomb,et al.  Backtrack Programming , 1965, JACM.

[27]  Toby Walsh,et al.  The Tractability of Global Constraints , 2004, CP.

[28]  Alan Borning,et al.  The Programming Language Aspects of ThingLab, a Constraint-Oriented Simulation Laboratory , 1981, TOPL.

[29]  Richard Fikes,et al.  REF-ARF: A System for Solving Problems Stated as Procedures , 1970, Artif. Intell..

[30]  P. Berlandier Improving domain filtering using restricted path consistency , 1995, Proceedings the 11th Conference on Artificial Intelligence for Applications.

[31]  Pascal Van Hentenryck,et al.  The Cardinality Operator: A New Logical Connective for Constraint Logic Programming , 1990, WCLP.

[32]  Marc Gyssens On the complexity of join dependencies , 1986, TODS.

[33]  Pascal Van Hentenryck Constraint satisfaction in logic programming , 1989, Logic programming.

[34]  Philippe Jégou,et al.  A filtering process for general constraint-satisfaction problems: achieving pairwise-consistency using an associated binary representation , 1989, [Proceedings 1989] IEEE International Workshop on Tools for Artificial Intelligence.

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

[36]  Edward P. K. Tsang,et al.  No more "Partial" and "Full Looking Ahead" , 1998, Artif. Intell..

[37]  Krzysztof R. Apt,et al.  The Essence of Constraint Propagation , 1998, Theor. Comput. Sci..

[38]  Alan K. Mackworth On Reading Sketch Maps , 1977, IJCAI.

[39]  Krzysztof R. Apt,et al.  Automatic Generation of Constraint Propagation Algorithms for Small Finite Domains , 1999, CP.

[40]  Richard J. Wallace,et al.  Why AC-3 is Almost Always Better than AC4 for Establishing Arc Consistency in CSPs , 1993, IJCAI.

[41]  Hilary Putnam,et al.  A Computing Procedure for Quantification Theory , 1960, JACM.

[42]  Christian Bessiere,et al.  Optimal and Suboptimal Singleton Arc Consistency Algorithms , 2005, IJCAI.

[43]  David L. Waltz,et al.  Generating Semantic Descriptions From Drawings of Scenes With Shadows , 1972 .

[44]  Rina Dechter,et al.  On the Expressiveness of Networks with Hidden Variables , 1990, AAAI.

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

[46]  Roland H. C. Yap,et al.  Arc Consistency on n-ary Monotonic and Linear Constraints , 2000, CP.

[47]  Eugene C. Freuder,et al.  Ordering Heuristics for Arc Consistency Algorithms , 1992 .

[48]  Peter van Beek,et al.  Local and Global Relational Consistency , 1995, Theor. Comput. Sci..

[49]  Rina Dechter,et al.  Network-Based Heuristics for Constraint-Satisfaction Problems , 1987, Artif. Intell..

[50]  Peter van Beek,et al.  An Efficient Bounds Consistency Algorithm for the Global Cardinality Constraint , 2005, Constraints.

[51]  Toby Walsh Relational Consistencies , 2001 .

[52]  Sharad Malik,et al.  Chaff: engineering an efficient SAT solver , 2001, Proceedings of the 38th Design Automation Conference (IEEE Cat. No.01CH37232).

[53]  Donald E. Knuth,et al.  The Problem of Compatible Representatives , 1992, SIAM J. Discret. Math..

[54]  Toby Walsh,et al.  Handbook of Constraint Programming , 2006, Handbook of Constraint Programming.

[55]  Philippe Jégou,et al.  On the Consistency of General Constraint-Satisfaction Problems , 1993, AAAI.

[56]  Lakhdar Sais,et al.  About the use of local consistency in solving CSPs , 2000, Proceedings 12th IEEE Internationals Conference on Tools with Artificial Intelligence. ICTAI 2000.

[57]  Christian Bessiere,et al.  Using Inference to Reduce Arc Consistency Computation , 1995, IJCAI.

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

[59]  Thomas C. Henderson,et al.  Arc and Path Consistency Revisited , 1986, Artif. Intell..

[60]  M. Morris,et al.  The Design , 1998 .

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

[62]  Toby Walsh,et al.  Decomposable Constraints , 1999, New Trends in Constraints.

[63]  Chu Min Li,et al.  Heuristics Based on Unit Propagation for Satisfiability Problems , 1997, IJCAI.

[64]  Andreas Podelski,et al.  Constraint Programming: Basics and Trends , 1995, Lecture Notes in Computer Science.

[65]  Jean-Louis Laurière,et al.  A Language and a Program for Stating and Solving Combinatorial Problems , 1978, Artif. Intell..

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

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

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

[69]  Roland H. C. Yap,et al.  An optimal coarse-grained arc consistency algorithm , 2005, Artif. Intell..

[70]  Mihalis Yannakakis,et al.  The complexity of facets (and some facets of complexity) , 1982, STOC '82.

[71]  Yishai A. Feldman,et al.  Portability by automatic translation: a large-scale case study , 1999 .

[72]  Christian Bessiere,et al.  Arc-Consistency and Arc-Consistency Again , 1993, Artif. Intell..

[73]  Christian Bessiere,et al.  A Generic Customizable Framework for Inverse Local Consistency , 1999, AAAI/IAAI.

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

[75]  Olivier Lhomme,et al.  An Efficient Filtering Algorithm for Disjunction of Constraints , 2003, CP.

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

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

[78]  Roland H. C. Yap,et al.  Making AC-3 an Optimal Algorithm , 2001, IJCAI.

[79]  Roman Barták,et al.  A New Algorithm for Singleton Arc Consistency , 2004, FLAIRS.

[80]  Martin C. Cooper An Optimal k-Consistency Algorithm , 1989, Artif. Intell..

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

[82]  Chia-Hoang Lee,et al.  Comments on Mohr and Henderson's Path Consistency Algorithm , 1988, Artif. Intell..

[83]  Eugene C. Freuder Completable Representations of Constraint Satisfaction Problems , 1991, KR.

[84]  Hélène Collavizza,et al.  A Note on Partial Consistencies over Continuous Domains , 1998, CP.

[85]  Jeanine Weekes Schroer,et al.  The Finite String Newsletter Abstracts of Current Literature Glisp User's Manual , 2022 .

[86]  Olivier Lhomme,et al.  Consistency Techniques for Numeric CSPs , 1993, IJCAI.

[87]  M. R. C. van Dongen,et al.  Improving Arc-Consistency Algorithms with Double-Support Checks , 2000 .

[88]  Catriel Beeri,et al.  On the Desirability of Acyclic Database Schemes , 1983, JACM.

[89]  Thi-Bich-Hanh Dao,et al.  Indexical-Based Solver Learning , 2002, CP.

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

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

[92]  Moninder Singh Path Consistency Revisited , 1996, Int. J. Artif. Intell. Tools.

[93]  Hachemi Bennaceur,et al.  Partition-k-AC: An Efficient Filtering Technique Combining Domain Partition and Arc Consistency , 2001, CP.

[94]  Donald E. Knuth,et al.  Semantics of context-free languages , 1968, Mathematical systems theory.

[95]  Eugene C. Freuder A sufficient condition for backtrack-bounded search , 1985, JACM.

[96]  Toby Walsh,et al.  Propagating Logical Combinations of Constraints , 2005, IJCAI.

[97]  J. J. McGregor Relational consistency algorithms and their application in finding subgraph and graph isomorphisms , 1979, Inf. Sci..

[98]  Christophe Lecoutre,et al.  Exploiting Multidirectionality in Coarse-Grained Arc Consistency Algorithms , 2003, CP.

[99]  Rina Dechter,et al.  Tree Clustering for Constraint Networks , 1989, Artif. Intell..

[100]  François Pachet,et al.  Automatic Generation of Music Programs , 1999, CP.

[101]  Christian Bessiere,et al.  Arc Consistency for General Constraint Networks: Preliminary Results , 1997, IJCAI.

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

[103]  Krzysztof R. Apt,et al.  Principles of constraint programming , 2003 .

[104]  Eugene C. Freuder,et al.  Selective relaxation for constraint satisfaction problems , 1991, [Proceedings] Third International Conference on Tools for Artificial Intelligence - TAI 91.

[105]  Christian Bessiere,et al.  Using Constraint Metaknowledge to Reduce Arc Consistency Computation , 1999, Artif. Intell..

[106]  Pascal Van Hentenryck,et al.  CLP(Intervals) Revisited , 1994, ILPS.

[107]  Jean-François Puget,et al.  A Fast Algorithm for the Bound Consistency of alldiff Constraints , 1998, AAAI/IAAI.

[108]  Pascal Van Hentenryck,et al.  To Be or Not to Be ... a Global Constraint , 2003, CP.

[109]  Christian Bessiere,et al.  Theoretical Analysis of Singleton Arc Consistency , 2004 .

[110]  Horst Bunke,et al.  Syntactic and Structural Pattern Recognition , 1988, NATO ASI Series.

[111]  Vipin Kumar,et al.  Search in Artificial Intelligence , 1988, Symbolic Computation.

[112]  J. Freeman Improvements to propositional satisfiability search algorithms , 1995 .

[113]  Christian Bessiere,et al.  Domain Filtering Consistencies , 2011, J. Artif. Intell. Res..

[114]  Peter J. Stuckey,et al.  When do bounds and domain propagation lead to the same search space , 2001, PPDP '01.

[115]  Romuald Debruyne A Property of Path Inverse Consistency Leading to an Optimal PIC Algorithm , 2000, ECAI.

[116]  Roger Mohr,et al.  Running efficiently arc consistency , 1986 .

[117]  Toby Walsh,et al.  The Complexity of Global Constraints , 2004, AAAI.