## On the Minimality and Global Consistency of Row-Convex Constraint Networks (1992)

Citations: | 50 - 3 self |

### BibTeX

@MISC{Beek92onthe,

author = {Peter van Beek and Rina Dechter},

title = {On the Minimality and Global Consistency of Row-Convex Constraint Networks},

year = {1992}

}

### Years of Citing Articles

### OpenURL

### Abstract

Constraint networks have beenshown 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) nd a solution that satis es the constraints and (ii) nd 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 e ciently and we show, by examining

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