The complexity of constraint satisfaction: an algebraic approach

Many computational problems arising in artificial intelligence, computer science and elsewhere can be represented as constraint satisfaction and optimization problems. In this survey paper we discuss an algebraic approach that has proved to be very successful in studying the complexity of constraint problems. 1 Constraint satisfaction problems The constraint satisfaction problem (CSP) is a powerful general framework in which a variety of combinatorial problems can be expressed [20, 59, 61, 79]. The aim in a constraint satisfaction problem is to find an assignment of values to the variables, subject to specified constraints. In artificial intelligence, this framework is widely acknowledged as a convenient and efficient way of modelling and solving a number of real-world problems such as planning [48] and scheduling [75], frequency assignment problems [27], image processing [63], programming language analysis [65] and natural language understanding [2]. In database theory, it has been shown that the key problem of conjunctive-query evaluation can be viewed as