Assef Chmeiss

EFFICIENT PATH-CONSISTENCY PROPAGATION

Recently, efficient algorithms have been proposed to achieve arc- and path-consistencey in constraint networks. For example, for arc-consistency, there are linear time algorithms (in the size of the problem) which are efficient in practice (e.g. AC-6 and AC-7). The best path-consistency algorithm proposed is PC-{5|6} which is a natural generalization of AC-6 to path-consistency. While its theoretical complexity is the best, experimentations show clearly that it is not very efficient in practice. In this paper, we propose two algorithms, one for arc-consistency, AC-8, and the second for path-consistency, PC-8. These algorithms are based on the same principle: to exploit minimal supports as AC-6 and PC-{5|6} do, but without recording them. While for AC-8, this approach is of limited interest, we show that for path-consistency, this new approach allows to outperform significantly existing algorithms.

Neighborhood-Based Variable Ordering Heuristics for the Constraint Satisfaction Problem

One of the key factors in the efficiency of backtracking algorithms is the rule they use to decide on which variable to branch next (namely, the variable ordering heuristics). In this paper, we give a formulation of dynamic variable ordering heuristics that takes into account the properties of the neighborhood of the variable.

Consistency of Triangulated Temporal Qualitative Constraint Networks

In this paper, we introduce for the qualitative constraint networks (QCNs) a new consistency: the partial weak composition consistency. The partial weak composition consistency, similarly to the partial path-consistency, considers triangles of a graph and corresponds to the weak composition consistency restricted to these triangles. We show that for the pre-convex QCNs of the Interval Algebra (IA), the partial weak composition consistency with respect to a triangulation of the graph of constraints is sufficient to decide the consistency problem. From this result, we propose an algorithm allowing to solve QCNs of IA. The experiments that we have conducted show the interest of this algorithm to solve the consistency problem of the QCNs of IA.

Constraint satisfaction problems : backtrack search revisited

Many backtrack search algorithms has been designed over the last years to solve constraint satisfaction problems. Among them, Forward Checking (FC) and Maintaining Arc Consistency (MAC) algorithms are the most popular and studied algorithms. In This work, such algorithms are revisited and extensively compared giving rise to interesting characterization of their efficiency with respect to random instances. More precisely, we provide experimental evidence that FC outperforms MAC on hard CSPs with high graph density and low constraint tightness whereas MAC is better on hard CSPs with low density and high constraints tightness. This results show that on some CSPs maintaining full arc consistency during search might be time consuming. Then, we propose a new generic approach that maintain partial and parameterizable form of local consistency.

A generalization of chordal graphs and the maximum clique problem

Abstract A graph is chordal or triangulated if it has no chordless cycle with four or more vertices. Chordal graphs are well known for their combinatorial and algorithmic properties. Here we introduce a generalization of chordal graphs, namely CSGk graphs. Informally, a CSG0 graph is a complete graph, and for k s> 0, the class of CSGk graphs is defined inductively in a such manner that CSG1 Graphs are chordal graphs. We show that CSGk Graphs inherit of the same kind of properties as chordal graph. As a consequence, we show that the maximum clique problem is polynomial on CSGk graphs while this problem is NP-hard in the general case.

About the use of local consistency in solving CSPs

Local consistency is often a suitable paradigm for solving constraint satisfaction problems. We show how search algorithms could be improved, thanks to a smart use of two filtering techniques (path consistency and singleton arc consistency). We propose a possible way to get benefits from using a partial form of path consistency (PC) during the search. We show how local treatment based on singleton arc consistency (SAC) can be used to achieve more powerful pruning.

Two new constraint propagation algorithms requiring small space complexity

Recently, efficient algorithms have been proposed to achieve arc- and path-consistency in constraint networks. The best path-consistency algorithm proposed is PE-{5|6} which is a natural generalization of AC-6 to path-consistency independently proposed by M. Singh (1995) for PC-5 and A. Chmeiss and P. Jegou (1995) for PC-6. Unfortunately, we have remarked that PC-{5|6}, though it is widely better than PC-4 (Chmeiss and P. Jegou, 1996) was not very efficient in practice, especially for those classes of problems that require an important space to be run. So, we propose a new path-consistency algorithm called PC-8, the space complexity of which is O(n/sup 2/d) but its time complexity is O(n/sup 3/d/sup 4/), i.e. worse than that of PC-{5|6}. However, the simplicity of PC-8 as well as the data structures used for its implementation offer a higher performance than PC-{5|6}. The principle of PC-8 is also used to propose a new algorithm to achieve arc-consistency called AC-8.

Light Integration of Path Consistency for Solving CSPs

Many local consistency properties have been exploited in solving constraint satisfaction problems. The objective is to reduce the search space and consequently improve search methods. It has been shown that maintaining arc- consistency during search is very useful in solving CSPs. The use of stronger local consistency forms (like path consistency) is still limited since they need complicated data structures to be managed and the constraint graph may be modified. In this paper, we propose a possible way to get benefits from using, in a preprocessing step, a partial form of path consistency and arc consistency based on support intervals notion.

About Look-Ahead Algorithms in Constraint Satisfaction Problems

Many problems in Artificial Intelligence can be solved using the Constraint Satisfaction Problems (CSPs) techniques. CSPs are, generally, solved using backtrack based algorithms. A large variety of algorithms has been proposed to deal with CSPs. In this paper, we focus on the look-ahead algorithms in CSPs (namely the most popular ones: Forward-Checking and Maintaining Arc-Consistency), and we propose a generic approach which maintains a restricted form of arc-consistency during the search process. We also give a way to exploit another form of local consistency: the Directed Path-Consistency.