Constraint-based reasoning is a paradigm for formulating knowledge as a set of constraints without specifying the method by which these constraints are to be satisfied. A variety of techniques have been developed for finding partial or complete solutions for different kinds of constraint expressions. These have been successfully applied to diverse tasks such as design, diagnosis, truth maintenance, scheduling, spatiotemporal reasoning, logic programming and user interface. Constraint networks are graphical representations used to guide strategies for solving constraint satisfaction problems (CSPs).

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.

There has been substantial recent interest in two new families of search techniques. One family consists of nonsystematic methods such as gsat; the other contains systematic approaches that use a polynomial amount of justification information to prune the search space. This paper introduces a new technique that combines these two approaches. The algorithm allows substantial freedom of movement in the search space but enough information is retained to ensure the systematicity of the resulting analysis. Bounds are given for the size of the justification database and conditions are presented that guarantee that this database will be polynomial in the size of the problem in question. 1 INTRODUCTION The past few years have seen rapid progress in the development of algorithms for solving constraintsatisfaction problems, or csps. Csps arise naturally in subfields of AI from planning to vision, and examples include propositional theorem proving, map coloring and scheduling problems. The probl...

problem (csp), namely, naive backtracking (BT), backjumping (BJ), conflict-directed backjumping

General purpose truth maintenance systems have received considerable attention in the past few years. This paper discusses the functionality of truth maintenance systems and compares various existing algorithms. Applications and directions for future research are also discussed. Introduction In 1978 Jon Doyle wrote a masters thesis at the MIT AI Laboratory entitled "Truth Maintenance Systems for Problem Solving" [ Doyle, 1979 ] . In this thesis Doyle described an independent module called a truth maintenance system, or TMS, which maintained beliefs for general problem solving systems. In the twelve years since the appearance of Doyle's TMS a large body of literature has accumulated on truth maintenance. The seminal idea appears not to have been any particular technical mechanism but rather the general concept of an independent module for truth (or belief) maintenance. All truth maintenance systems manipulate proposition symbols and relationships between proposition symbols. I will use...

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...

Over the years a large number of algorithms has been discovered to solve instances of CSP problems. In a recent paper Prosser [9] proposed a new approach to these algorithms by splitting them up in groups with identical forward (Backtracking, Backjumping, Conflict-Directed Backjumping) and backward (Backtracking, Backmarking, Forward Checking) moves. By combining the forward move of an algorithm from the first group and the backward move of an algorithm from the second group he was able to develop four new hybrid algorithms: Backmarking with Backjumping (BMJ), Backmarking with Conflict-Directed Backjumping (BMCBJ) , Forward Checking with Backjumping (FC-BJ) and Forward Checking with Conflict-Directed Backjumping (FC-CBJ). Variable reordering heuristics have been suggested by, among others, by Haralick [6] and Purdom [11, 14] to improve the standard CSP algorithms. They obtained both analytical and empiral results about the performance of these heuristics in their research. In this thes...

Several graph parameters such as induced width, minimum maximum clique size of a chordal completion, k-tree number, bandwidth, front length or minimum pseudo-tree height are available in the CSP community to bound the complexity of specific CSP instances using dedicated algorithms. After an introduction to the main algorithms that can exploit these parameters, we try to exhaustively review existing parameters and the relations that may exist between then. In the process we exhibit some missing relations. Several existing results, both old results and recent results from graph theory and Cholesky matrix factorization technology [BGHK95] allow us to give a very dense map of relations between these parameters. These results strongly relate several existing algorithms and answer some questions which were considered as open in the CSP community. Warning: this document is a working paper. Some sections may be incomplete or currently being worked out ([GJC94] degree of cyclicity not ...

. Exact and inexact methods can be used for solving Constraint Satisfaction Problems (CSP), i.e. for finding a variable assignment which violates none of the constraints or minimizes the number of violated constraints. Based on a Backtrack tree search, exact methods are able to produce an optimal assignment, when no time limit is imposed. Based on local improvement mechanisms, inexact methods cannot guarantee that, but may produce better quality assignments in a limited time. In this paper, we show how an inexact method, coming from statistical physics, and more precisely from the Mean Field Theory, can boost an exact method by providing it with a good quality assignment, whose valuation can be used as an initial upper bound, and with two heuristics for ordering variables and values. Experiments on randomly generated classical and partial CSPs show significative gains in terms of time, even when adding the times used by both the Mean Field and the Backtrack methods. 1 Motivation The ...

Generally, constraint satisfaction problems (CSP) are NP-complete. Many subclasses, however, can be solved efficiently. They are mainly defined by properties of the variable domains, the constraint semantics, the constraint graph structures or a combination of those. In this paper, we consider a new aspect of making a CSP feasible, namely the dynamic essence of the problem modeling process. As a case study, we analyze the assembly problem, ie the spatial joining of separate rigid bodies within a mechanical construction. We show how insight into the modeling process helps to build an efficient assembly solver. In particular, this solver takes advantage of the restricted complexity of completed constructions as well as of the specific information requirements during the modeling process. 1 Introduction Generally, constraint solving and also dynamic constraint solving are difficult. But often one can detect feasible subclasses defined by special properties: ffl restricted varia...