The alldifferent Constraint: A Survey

The constraint of difference is known to the constraint programming community since Lauriere introduced Alice in 1978. Since then, several solving strategies have been designed for this constraint. In this paper we give both a practical overview and an abstract comparison of these different strategies.Comment: 12 pages, 3 figures, paper accepted at the 6th Annual workshop of the ERCIM Working Group on Constraint

Parallelism in Constraint Programming

Writing efficient parallel programs is the biggest challenge of the software industry for the foreseeable future. We are currently in a time when parallel computers are the norm, not the exception. Soon, parallel processors will be standard even in cell phones. Without drastic changes in hardware development, all software must be parallelized to its fullest extent. Parallelism can increase performance and reduce power consumption at the same time. Many programs will execute faster on a dual-core processor than a single core processor running at twice the speed. Halving the speed of a processor can reduce the power consumption up to four times. Hence, parallelism gives more performance per unit of power to efficient programs. In order to make use of parallel hardware, we need to overcome the difficulties of parallel programming. To many programmers, it is easier to learn a handful of small domain-specific programming languages than to learn efficient parallel programming. The frameworks for these languages can then automatically parallelize the program. Automatically parallelizing traditional programs is usually much more difficult. In this thesis, we study and present parallelism in constraint programming (CP). We have developed the first constraint framework that automatically parallelizes both the consistency and the search of the solving process. This allows programmers to avoid the difficult issues of parallel programming. We also study distributed CP with independent agents and propose solutions to this problem. Our results show that automatic parallelism in CP can provide very good performance. Our parallel consistency scales very well for problems with many large constraints. We also manage to combine parallel consistency and parallel search with a performance increase. The communication and load-balancing schemes we developed increase the scalability of parallel search. Our model for distributed CP is orders of magnitude faster than traditional approaches. As far as we know, it is the first to solve standard benchmark scheduling problems

Intermediary Local Consistencies

International audienceWe propose a new definition for characterizing levels of consistency. A perspective is to provide new tools for classifying filtering algorithms, including incomplete algorithms based on the semantics of constraints

Parallel consistency in constraint programming

Program parallelization becomes increasingly important when new multi-core architectures provide ways to improve performance. One of the greatest challenges of this development lies in programming parallel applications. Using declarative languages, such as constraint programming, can make the transition to parallelism easier by hiding the parallelization details in a framework. Automatic parallelization in constraint programming has previously focused on data parallelism. In this paper, we look at task parallelism, specifically the case of parallel consistency. We have developed two models of parallel consistency, one that shares intermediate results and one that does not. We evaluate which model is better in our experiments. Our results show that parallelizing consistency can provide the programmer with a robust scalability for regular problems with global constraints

Propagating Conjunctions of AllDifferent Constraints

We study propagation algorithms for the conjunction of two AllDifferent constraints. Solutions of an AllDifferent constraint can be seen as perfect matchings on the variable/value bipartite graph. Therefore, we investigate the problem of finding simultaneous bipartite matchings. We present an extension of the famous Hall theorem which characterizes when simultaneous bipartite matchings exists. Unfortunately, finding such matchings is NP-hard in general. However, we prove a surprising result that finding a simultaneous matching on a convex bipartite graph takes just polynomial time. Based on this theoretical result, we provide the first polynomial time bound consistency algorithm for the conjunction of two AllDifferent constraints. We identify a pathological problem on which this propagator is exponentially faster compared to existing propagators. Our experiments show that this new propagator can offer significant benefits over existing methods.Comment: AAAI 2010, Proceedings of the Twenty-Fourth AAAI Conference on Artificial Intelligenc

Finite Domain Bounds Consistency Revisited

A widely adopted approach to solving constraint satisfaction problems combines systematic tree search with constraint propagation for pruning the search space. Constraint propagation is performed by propagators implementing a certain notion of consistency. Bounds consistency is the method of choice for building propagators for arithmetic constraints and several global constraints in the finite integer domain. However, there has been some confusion in the definition of bounds consistency. In this paper we clarify the differences and similarities among the three commonly used notions of bounds consistency.Comment: 12 page

Making Bound Consistency as Effective as Arc Consistency

International audienceWe study under what conditions bound consistency (BC) and arc consistency (AC), two forms of propagation used in constraint solvers, are equivalent to each other. We show that they prune exactly the same values when the propagated constraint is connected row convex / closed under median and its complement is row convex. This characterization is exact for binary constraints. Since row convexity depends on the order of the values in the domains, we give polynomial algorithms for computing orders under which BC and AC are equivalent, if any