Jean-Charles Régin

Embarrassingly Parallel Search

We propose the Embarrassingly Parallel Search, a simple and efficient method for solving constraint programming problems in parallel. We split the initial problem into a huge number of independent subproblems and solve them with available workers, for instance cores of machines. The decomposition into subproblems is computed by selecting a subset of variables and by enumerating the combinations of values of these variables that are not detected inconsistent by the propagation mechanism of a CP Solver. The experiments on satisfaction problems and optimization problems suggest that generating between thirty and one hundred subproblems per worker leads to a good scalability. We show that our method is quite competitive with the work stealing approach and able to solve some classical problems at the maximum capacity of the multi-core machines. Thanks to it, a user can parallelize the resolution of its problem without modifying the solver or writing any parallel source code and can easily replay the resolution of a problem.

Improving GAC-4 for Table and MDD Constraints

We introduce GAC-4R, MDD-4, and MDD-4R three new algorithms for maintaining arc consistency for table and MDD constraints. GAC-4R improves the well-known GAC-4 algorithm by managing the internal data structures in a different way. Instead of maintaining the internal data structures only by studying the consequences of deletions, we propose to reset the data structures by recomputing them from scratch whenever it saves time. This idea avoids the major drawback of the GAC-4 algorithm, i.e., its cost at a shallow search-tree depth. We also show that this idea can be exploited in MDD constraints. Experiments show that GAC-4R is competitive with the best arc-consistency algorithms for table constraints, and that MDD-4R clearly outperforms all classical algorithms for table or MDD constraints.

Improvement of the Embarrassingly Parallel Search for Data Centers

We propose an adaptation of the Embarrassingly Parallel Search (EPS) method for data centers. EPS is a simple but efficient method for parallel solving of CSPs. EPS decomposes the problem in many distinct subproblems which are then solved independently by workers. EPS performed well on multi-cores machines (40), but some issues arise when using more cores in a datacenter. Here, we identify the decomposition as the cause of the degradation and propose a parallel decomposition to address this issue. Thanks to it, EPS gives almost linear speedup and outperforms work stealing by orders of magnitude using the Gecode solver.

Constructions and In-Place Operations for MDDs Based Constraints

This papers extends in three ways our previous work about efficient operations on Multi-valued Decision Diagrams (MDD) for building Constraint Programming models. First, we improve the existing methods for transforming a set of tuples, Global Cut Seeds or sequences of tuples into MDDs. Then, we present in-place algorithms for adding and deleting tuples from an MDD. Finally, we describe an incremental version of an algorithm which reduces an MDD. We show on a real-life application that in-place operations on MDDs combined with this incremental algorithm outperform classical operations. Furthermore, we give some experimental results showing that the creation algorithms we propose strongly improve upon existing ones.

MDDs: Sampling and Probability Constraints

We propose to combine two successful techniques of Artificial Intelligence: sampling and Multi-valued Decision Diagrams (MDDs). Sampling, and notably Markov sampling, is often used to generate data resembling to a corpus. However, this generation has usually to respect some additional constraints, for instance to avoid plagiarism or to respect some rules of the application domain. We propose to represent the corpus dependencies and these side constraints by an MDD and to develop some algorithms for sampling the solutions of an MDD while respecting some probabilities or a Markov chain. In that way, we obtain a generic method which avoids the development of ad-hoc algorithms for each application as it is currently the case. In addition, we introduce new constraints for controlling the probabilities of the solutions that are sampled. We experiments our method on a real life application: the geomodeling of a petroleum reservoir, and on the generation of French alexandrines. The obtained results show the advantage and the efficiency of our approach.

Parallel Constraint Programming.

Constraint programming (CP) is an efficient technique for solving combinatorial optimization problems. In CP a problem is defined over variables that take values in domains and constraints which restrict the allowed combination of values. CP uses for each constraint an algorithm that removes values of variables that are inconsistent with the constraint. These algorithms are called while a domain is modified. Then, a search algorithm such as a backtracking or branch-and-bound algorithm is called to find solutions. Several methods have been proposed to combine CP with parallelism. In this chapter, we present some of them: parallelization of the propagator, parallel propagation, search splitting, also called work-stealing, problem decomposition, also called embarrassingly parallel search (EPS), and portfolio approaches. We detail the two giving the best performances in practice: the work-stealing approach and embarrassingly parallel search. We give some experiments supporting this claim on a single multi-core machine, on a data center and on the cloud.