Constraint Satisfaction, Databases, and Logic

Constraint satisfaction problems constitute a broad class of algorithmic problems that are ubiquitous in several differ­ ent areas of artificial intelligence and computer science. In their full generality, constraint satisfaction problems are NP-complete and, thus, presumed to be algorithmically in­ tractable. To cope with the intractability of these prob­ lems, researchers have devoted considerable research efforts to both the design of heuristic algorithms for constraint sat­ isfaction and the pursuit of "islands of tractability", that is, special cases of constraint satisfaction problems for which polynomial-time algorithms exist. During the past decade, the pursuit of "islands of tractability" of constraint satisfaction has been intensified and has led to a number of discoveries that have also unveiled tight connections between constraint satisfaction, database theory, logic, and universal algebra. Our goal in this paper is to present an overview of the current state of affairs in the study of the computational complexity of constraint satisfaction with emphasis on the connections of this area of research with database theory and logic. The paper is organized as follows: Section 2 contains the precise definition of the C O N STRAINT SATISFACTION PROBLEM and its reformulation as the H O M O M O R P H I S M P R O B L E M ; Section 3 contains some of the connections between constraint satisfaction problems and database theory; the remaining Sections 4, 5, and 6 contain a high-level account of some of the main results about the computational complexity of constraint satisfaction and the pursuit of tractable cases of this problem.