A large variety of problems in Artificial Intelligence and other areas of computer science can be viewed as a special case of the constraint satisfaction problem. Some examples are machine vision, belief maintenance, scheduling, temporal reasoning, graph problems, floor plan design, planning genetic experiments, and the satisfiability problem. A number of different approaches have been developed for solving these problems. Some of them use constraint propagation to simplify the original problem. Others use backtracking to directly search for possible solutions. Some are a combination of these two techniques. This paper presents a brief overview of many of these approaches in a tutorial fashion.

In reasoning tasks involving the maintenance of consistent databases (so-called QQconstraint networks/Q/Q), it is customary to enforce local consistency conditions in order to simplify the subsequent construction of a globally coherent model of the data. In this paper we present a relationship between the sizes of the variables' domains, the constraints' arity and the level of local consistency sufficient to ensure global consistency. Based on these parameters a new tractability classification of constraint networks is presented. We also show, based on this relationship, that any relation on bi-valued variables which is not representable by a network of binary constraints cannot be represented by networks with any number of hidden variables.

Local consistency has proven to be an important concept in the theory and practice of constraint networks. In this paper, we present a new definition of local consistency, called relational consistency. The new definition is relation-based, in contrast with the previous definition of local consistency, which we characterize as variable-based. We show the conceptual power of the new definition by showing how it unifies known elimination operators such as resolution in theorem proving, joins in relational databases, and variable elimination for solving linear inequalities. Algorithms for enforcing various levels of relational consistency are introduced and analyzed. We also show the usefulness of the new definition in characterizing relationships between properties of constraint networks and the level of local consistency needed to ensure global consistency.

Finding solutions to a binary constraint satisfaction problem is known to be an NP-complete problem in general, but may be tractable in cases where either the set of allowed constraints or the graph structure is restricted. This paper considers restricted sets of contraints which are closed under permutation of the labels. We identify a set of constraints which gives rise to a class of tractable problems and give polynomial time algorithms for solving such problems, and for finding the equivalent minimal network. We also prove that the class of problems generated by any set of constraints not contained in this restricted set is NP-complete. 1 Introduction Finding solutions to a constraint satisfaction problem is known to be an NPcomplete problem in general [11] 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...

We consider constraint satisfaction problemswith variables in continuous,numerical domains. Contrary to most existing techniques, which focus on computing one single optimal solution, we address the problem of computing a compact representation of the space of all solutions admitted by the constraints. In particular, we show how globally consistent (also called decomposable) labelings of a constraint satisfaction problem can be computed.

The Constraint Satisfaction Problem is a type of combinatorial search problem of much interest in Artificial Intelligence and Operations Research. The simplest algorithm for solving such a problem is chronological backtracking, but this method suffers from a malady known as "thrashing," in which essentially the same subproblems end up being solved repeatedly. Intelligent backtracking algorithms, such as backjumping and dependency-directed backtracking, were designed to address this difficulty, but the exact utility and range of applicability of these techniques have not been fully explored. This dissertation describes an experimental and theoretical investigation into the power of these intelligent backtracking algorithms. We compare the empirical performance of several such algorithms on a range of problem distributions. We show that the more sophisticated algorithms are especially useful on those problems with a small number of constraints that happen to be difficult for chronologica...

We study the problems of deciding consistency and performing variable elimination for disjunctions of linear inequalities and disequations with at most one inequality per disjunction. This new class of constraints extends the class of generalized linear constraints originally studied by Lassez and McAloon. We show that deciding consistency of a set of constraints in this class can be done in polynomial time. We also present a variable elimination algorithm which is similar to Fourier's algorithm for linear inequalities. Finally, we use these results to provide new temporal reasoning algorithms for the Ord-Horn subclass of Allen's interval formalism. We also show that there is no low level of local consistency that can guarantee global consistency for the OrdHorn subclass. This property distinguishes the Ord-Horn subclass from the pointizable subclass (for which strong 5-consistency is sufficient to guarantee global consistency), and the continuous endpoint subclass (for whi...

Arc consistency algorithms are used in solving constraint satisfaction problems and are important in constraint logic programming languages. Search order heuristics for arc consistency algorithms significantly enhance the efficiency of their implementation. In this paper we propose and evaluate several ordering heuristics. Care is taken with experimental design, involving random problems, and statistical evaluation of results. A heuristic is identified which yields about 50% savings on average, using the standard measure of consistency pair checks, with reasonable heuristic computation cost. 1 Introduction Arc consistency insures that any two mutually constraining problem variables are mutually consistent: given a value for one, we can find a value for the other which satisfies the constraint between them. The constraint specifies which pairs of values can be simultaneously assumed by the pair of variables. Arc consistency is a fundamental concept in constraint-based reasoning [ Mack...

Although the constraint satisfaction problem is NP-complete in general, a number of constraint classes have been identified for which some fixed level of local consistency is sufficient to ensure global consistency. In this paper, we describe a simple algebraic property which characterises all possible constraint types for which strong k-consistency is sufficient to ensure global consistency, for each k ? 2. We give a number of examples to illustrate the application of this result. 1 Introduction The constraint satisfaction problem provides a framework in which it is possible to express, in a natural way, many combinatorial problems encountered in artificial intelligence and elsewhere. The aim in a constraint satisfaction problem is to find an assignment of values to a given set of variables subject to constraints on the values which can be assigned simultaneously to certain specified subsets of variables. The constraint satisfaction problem is known to be an NP-complete problem in ge...

In this report we discuss constraint satisfaction problems. These are problems in which values must be assigned to a collection of variables, subject to specified constraints. We focus specifically on problems in which the domain of possible values for each variable is finite. The report surveys the various conditions that have been shown to be sufficient to ensure tractability in these problems. These are broken down into three categories: ffl Conditions on the overall structure; ffl Conditions on the nature of the constraints; ffl Conditions on bounded pieces of the problem. 1 Introduction A constraint satisfaction problem is a way of expressing simultaneous requirements for values of variables. The study of constraint satisfaction problems was initiated by Montanari in 1974 [34], when he used them as a way of describing certain combinatorial problems arising in image-processing. It was quickly realised that the same general framework was applicable to a much wider class of probl...