Constraint networks have been shown to be useful in formulating such diverse problems as scene labeling, natural language parsing, and temporal reasoning. Given a constraint network, we often wish to (i) find a solution that satisfies the constraints and (ii) find the corresponding minimal network where the constraints are as explicit as possible. Both tasks are known to be NP-complete in the general case. Task (i) is usually solved using a backtracking algorithm, and task (ii) is often solved only approximately by enforcing various levels of local consistency. In this paper, we identify a property of binary constraints called row convexity and show its usefulness in deciding when a form of local consistency called path consistency is sufficient to guarantee that a network is both minimal and globally consistent. Globally consistent networks have the property that a solution can be found without backtracking. We show that one can test for the row convexity property efficiently and we show, by examining applications of constraint networks discussed in the literature, that our results are useful in practice. Thus, we identify a class of binary constraint networks for which we can solve both tasks (i) and (ii) efficiently. Finally, we generalize the results for binary constraint networks to networks with non-binary constraints. Copyright 1995 by ACM, Inc.
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Categories and Subject Descriptors: F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems -- computations on discrete structures; G.2.2 [Discrete Mathematics]: Graph Theory -- permutations and combinations; I.2.4 [Artificial Intelligence]: Knowledge Representation Formalisms and Methods -- relation systems
General Terms: Algorithms, Theory
Additional Key Words and Phrases: Consecutive ones property, constraint-based reasoning, constraint networks, constraint satisfaction problems, path consistency, relations, row convexity
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