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A Knowledge Representation for Constraint Satisfaction Problems
October 1993 (vol. 5 no. 5)
pp. 740-752

We present a general representation for problems that can be reduced to constraint satisfaction problems (CSP) and a model for reasoning about their solution. The novel part of the model is a constraint-driven reasoner that manages a set of constraints specified in terms of arbitrarily complex Boolean expressions and represented in the form of a dependency network. This dependency network incorporates control information (derived from the syntax of the constraints) that is used for constraint propagation, contains dependency information that can be used for explanation and for dependency-directed backtracking, and is incremental in the sense that if the problem specification is modified, a new solution can be derived by modifying the existing solution. The constraint-driven reasoner is coupled to a problem solver which contains information about the problem variables and preference orderings.

[1] C. Alexander,Notes on the Synthesis of Form. Cambridge, MA: Harvard University Press, 1964.
[2] V. Chvatal, "Edmonds polytopes and a hierarchy of combinatorial problems,"Discrete Mathematics, vol. 4, 1973.
[3] A. Croker, V. Dhar, and D. McAllester, "Dependency directed backtracking for generalized satisficing assignment problems," to appear inManagement Science. Available asTech. Report 190, Department of Information Systems, NYU, 1988.
[4] H. Crowder, E. Johnson, and M. Padberg, "Solving large-scale zeroone linear programming problems,"Operations Research, vol. 31, Sept.-Oct. 1983.
[5] G. Dantzig,Linear Programming and Extensions. Princeton, NJ: Princeton University Press, 1963.
[6] R. Dechter and J. Pearl, "Network-based heuristics for constraint-satisfaction problems,"Artificial Intell., vol. 34, pp. 1-37, 1988.
[7] R. Dechter, "Methodolgy for CSP's," Workshop on Constraint Processing, IJCAI, Detroit, MI, Aug. 1989.
[8] V. Dhar, and H. E. Pople, "Rule-based versus structure-based models for explaining and generating expert behavior,"Commun. ACM, vol. 30, pp. 542-555, 1987.
[9] V. Dhar and P. Ranganathan, "Experiments with an integer programming formulation of an expert system,"MCC Tech. Rep. ACA-AI-022-89, Austin, TX, Feb. 1989.
[10] J. Doyle, "A truth maintenance system,"Artificial Intelligence, June 1979.
[11] M. S. Fox, N. Sadeh, and C. Baykan, "Constrained heuristic search," inProc. Eleventh Int. Joint Conf. Artificial Intelligence, Detroit, MI, pp. 309-315, Aug. 1989.
[12] E. C. Freuder, "Synthesizing constraint expressions,"Comm. ACM, vol. 21, no. 11, pp. 958-966, 1978.
[13] R.E. Gomory, "Outline of an algorithm for integer solutions to linear programs, " in R.L. Graves and P. Wolfe, Eds.,Recent Advances in Mathematical Programming. New York: McGraw-Hill, 1963.
[14] J.W. Goodwin, "A process theory of non-monotonic inference,"Proc. Ninth Int. Joint Conf. Artificial Intelligence, 1985.
[15] M. Grotschel and M. Padberg,The Travelling Salesman Problem: A Guided Tour of Combinatorial Optimization. New York: Wiley, 1982.
[16] P. Hansen, "Methods of nonlinear 0-1 programming,"Annals of Discrete Mathematicsvol. 5, pp. 53-70, 1974.
[17] R.M. Haralick and G.L. Elliot, "Increasing tree search efficiency for constraint satisfaction,"Artificial Intelligence, vol. 14, pp. 263-313, Aug. 1980.
[18] G.E Hinton, "Relaxation and its role in vision," Ph.D dissertation,University of Edinburgh, 1977.
[19] J. N. Hooker, "A quantitative approach to logical inference,"Decision Support Syst., vol 4, no 1, 1988.
[20] N. Karmarker, "A New Polynomial-Time Algorithm for Linear Programming,"Combinatorica, Vol. 4, No. 4, 1984, pp. 373-395.
[21] A. Mackworth, "Consistency in networks of relations,"Artificial Intelligence, vol. 8, pp. 99-118, 1977.
[22] D. McAllester, "Reasoning utility package,"AI Laboratory Memo 667, Apr. 1982.
[23] U. Montanari, "Networks of constraints: Fundamental properties and application to picture processing,"Information Science, vol. 7, 1974.
[24] U. Montanari and F. Rossi, "Constraint relaxation may be perfect,"Artificial Intelligence, to be published.
[25] B. Nudel, "Consistent labeling problems and their algorithms: Expected-complexities and theory-based heuristics,"Artificial Intelligence, vol. 21, pp. 135-178, 1983.
[26] B. Nudel, "Solving the general consistent labeling problem: Two algorithms and their expected complexities," inProc. National Conf. Artificial Intelligence, Aug. 1983.
[27] C. Petrie, D. Russinoff, and D. Steiner, "Proteus 2: System description,"MCC Tech. Rep. AI-136-87, May 1987.
[28] M. Reinfrank, "Lecture notes on reason maintenance systems," Tech.Rep. INF2 ARM-5-88, Siemens AG, 1988.
[29] W. R. Reitman,Cognition and Thought. New York: Wiley, 1965.
[30] H. Simon, "The structure of ill-structured problems,"Artificial Intelligence, vol. 4, Sept. 1973.
[31] D. Waltz, "Understanding line drawings of scenes with shadows," in P.H. Winston, Ed.,The-Psychology of Computer Vision. New York: McGraw-Hill, 1975, pp. 19-91.
[32] L.J. Watters, "Reduction of integer polynomial programming problems to zero-one linear programming problems,"Operations Research, vol. 15, 1967, pp. 1171-1174.

Index Terms:
knowledge representation; constraint satisfaction problems; constraint-driven reasoner; Boolean expressions; dependency network; control information; preference orderings; constraint handling; inference mechanisms; knowledge representation
Citation:
A.E. Croker, V. Dhar, "A Knowledge Representation for Constraint Satisfaction Problems," IEEE Transactions on Knowledge and Data Engineering, vol. 5, no. 5, pp. 740-752, Oct. 1993, doi:10.1109/69.243506
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