Frédéric Boussemart

Random constraint satisfaction: Easy generation of hard (satisfiable) instances

In this paper, we show that the models of random CSP instances proposed by Xu and Li [K. Xu, W. Li, Exact phase transitions in random constraint satisfaction problems, Journal of Artificial Intelligence Research 12 (2000) 93-103; K. Xu, W. Li, Many hard examples in exact phase transitions with application to generating hard satisfiable instances, Technical report, CoRR Report cs.CC/0302001, Revised version in Theoretical Computer Science 355 (2006) 291-302] are of theoretical and practical interest. Indeed, these models, called RB and RD, present several nice features. First, it is quite easy to generate random instances of any arity since no particular structure has to be integrated, or property enforced, in such instances. Then, the existence of an asymptotic phase transition can be guaranteed while applying a limited restriction on domain size and on constraint tightness. In that case, a threshold point can be precisely located and all instances have the guarantee to be hard at the threshold, i.e., to have an exponential tree-resolution complexity. Next, a formal analysis shows that it is possible to generate forced satisfiable instances whose hardness is similar to unforced satisfiable ones. This analysis is supported by some representative results taken from an intensive experimentation that we have carried out, using complete and incomplete search methods.

Backjump-based techniques versus conflict-directed heuristics

We present a general algorithm which gives a uniform view of several state-of-the-art systematic backtracking search algorithms for solving both binary and nonbinary CSP instances. More precisely, this algorithm integrates the most usual or/and sophisticated look-back and look-ahead schemes. By means of this algorithm, our purpose is then to study the interest of backjump-based techniques with respect to conflict-directed variable ordering heuristics.

Exploiting multidirectionality in coarse-grained arc consistency algorithms

Arc consistency plays a central role in solving Constraint Satisfaction Problems. This is the reason why many algorithms have been proposed to establish it. Recently, an algorithm called AC2001 and AC3.1 has been independently presented by their authors. This algorithm which is considered as a refinement of the basic algorithm AC3 has the advantage of being simple and competitive. However, it does not take into account constraint bidirectionality as AC7 does. In this paper, we address this issue, and, in particular, introduce two new algorithms called AC3.2 and AC3.3 which benefit from good properties of both AC3 and AC7. Indeed, AC3.2 and AC3.3 are as easy to implement as AC3 and take advantage of bidirectionality as AC7 does. More precisely, AC3.2 is a general algorithm which partially exploits bidirectionality whereas AC3.3 is a binary algorithm which fully exploits bidirectionality. It turns out that, when Maintaining Arc Consistency during search, MAC3.2, due to a memorization effect, is more efficient than MAC3.3 both in terms of constraint checks and cpu time. Compared to MAC2001/3.1, our experimental results show that MAC3.2 saves about 50% of constraint checks and, on average, 15% of cpu time.

AbsCon: A Prototype to Solve CSPs with Abstraction

In this paper, we present a Java constraint programming prototype called AbsCon which has been conceived to deal with CSP abstraction. AbsCon considers n-ary constraints and implements different value and variable ordering heuristics as well as different propagation methods. As AbsCon exploits object technology, it is easy to extend its functionalities.

A CSP Abstraction Framework

Many works about abstraction of Constraint Satisfaction Problems (CSPs) introduce materials in order to build specific abstractions. But, to our best knowledge, only two works [2] [9] were devoted to defining frameworks of CSP abstraction. In this paper, we try to go one step beyond by proposing an original and unifying framework with a two-fold objective: a proposal sufficiently general to embrace previous works and to envision new forms of abstraction, and sufficiently precise to decide without any ambiguity the correctness of a given abstraction.

Solving the cyclic job shop scheduling problem with linear precedence constraints using CP techniques

A cyclic scheduling problem is a problem which, under the requirement of respecting a finite set of constraints consists of ordering a finite set of tasks occurring in an indefinite number of times. In this paper, we propose, by employing different techniques that have been developed by the constraint programming (CP) community, to attack the cyclic job shop scheduling problem with linear precedence constraints. Indeed, this problem can be cut as a constraint satisfaction problem or a constraint optimization problem. By limiting the periodicity of the searched solution, we show that a complete tree search approach is viable since it allows giving satisfactory results while minimizing the overall execution time. Furthermore, such a solution is more adaptable to an industrial context since a limited periodicity can be easily exploited.

Implicit random constraint satisfaction problem

Random CSPs (constraint satisfaction problems) provide interesting benchmarks for experimental evaluation of algorithms. From a theoretical point of view, a lot of recent works have contributed to guarantee the existence of a so-called phase transition and, consequently, of hard and large problem instances. From a practical point of view, due to exponential space complexity, a vast majority of experiments based on random CSPs concerns binary problems. In this paper, we introduce a model of implicit random CSPs, i.e., of random CSPs where constraints are not given in extension but defined by a predicate. This new model involves an easy implementation, no space requirement and the possibility to perform experiments with large arity constraints.

Combining Nogoods in Restart-Based Search

Nogood recording is a form of learning that has been shown useful for solving constraint satisfaction problems. One simple approach involves recording nogoods that are extracted from the rightmost branches of the successive trees built by a backtrack search algorithm with restarts. In this paper, we propose several mechanisms to reason with so-called increasing-nogoods that exactly correspond to the states reached at the end of each search run. Interestingly, some similarities that can be observed between increasing-nogoods allow us to propose new original ways of dynamically combining them in order to improve the overall filtering capability of the learning system. Our preliminary results show the practical interest of our approach.

Efficient Constraint Propagation for Graph Coloring

Abstract In this paper, we investigate constraint propagation, a mechanism that is run at each basic step of a backtrack search algorithm such as the popular MAC. From a statistical analysis of some relevant features concerning propagation on a large set of graph coloring instances, we show that it is possible to make reasonable predictions about the capability of constraint propagation to detect inconsistency. Using this observation in order to control propagation effort, we show its practical effectiveness.