Abstract

. Many combinatorial search problems may be expressed as constraint satisfaction problems, and this class of problems is known to be NP-complete in general. In this paper we examine restricted classes of constraints which lead to tractable problems. We show that all known classes with this property may be characterized by a simple algebraic closure condition. Using this condition provides a uniform test to establish whether a given set of constraints falls into any of the known tractable classes, and may therefore be solved efficiently. 1 Introduction Many combinatorial search problems may be expressed as constraint satisfaction problems. Unfortunately, finding solutions to a constraint satisfaction problem is known to be an NP-complete problem in general [12] even when the constraints are restricted to binary constraints. However, many of the problems which arise in practice have special properties which allow them to be solved efficiently. The question of identifying restrictions t...

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