A test for tract ability

Abstract

Many combinatorial search problems can be expressed as 'constraint satisfaction problems', and this class of problems is known to be NP-complete in general. In this paper we investigate restricted classes of constraints which give rise to tractable problems. We show that any set of constraints must satisfy a certain type of algebraic closure condition in order to avoid NP-completeness. We also describe a simple test which can be applied to establish whether a given set of constraints satisfies a condition of this kind. The test involves solving a particular constraint satisfaction problem, which we call an 'indicator problem'.