## On Binary Constraint Problems (1994)

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Venue: | Journal of the ACM |

Citations: | 87 - 2 self |

### BibTeX

@ARTICLE{Ladkin94onbinary,

author = {Peter B. Ladkin and Roger D. Maddux},

title = {On Binary Constraint Problems},

journal = {Journal of the ACM},

year = {1994},

volume = {41},

pages = {435--469}

}

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### Abstract

The concepts of binary constraint satisfaction problems can be naturally generalized to the relation algebras of Tarski. The concept of path-consistency plays a central role. Algorithms for path-consistency can be implemented on matrices of relations and on matrices of elements from a relation algebra. We give an example of a 4-by-4 matrix of infinite relations on which no iterative local path-consistency algorithm terminates. We give a class of examples over a fixed finite algebra on which all iterative local algorithms, whether parallel or sequential, must take quadratic time. Specific relation algebras arising from interval constraint problems are also studied: the Interval Algebra, the Point Algebra, and the Containment Algebra. 1 Introduction The logical study of binary relations is classical [8], [9], [51], [52], [56], [53], [54]. Following this tradition, Tarski formulated the theory of binary relations as an algebraic theory called relation algebra [59] 1 . Constraint satis...