Domain k-Wise Consistency Made as Simple as Generalized Arc Consistency

Abstract. In Constraint Programming (CP), Generalized Arc Consistency (GAC) is the central property used for making inferences when solving Constraint Satisfaction Problems (CSPs). Developing simple and practical filtering algorithms based on consistencies stronger than GAC is a challenge for the CP community. In this paper, we propose to combine k-Wise Consistency (kWC) with GAC, where kWC states that every tuple in a constraint can be extended to every set of k − 1 additional constraints. Our contribution is as follows. First, we derive a domain-filtering consistency, called Domain k-Wise Consistency (DkWC), from the combination of kWC and GAC. Roughly speaking, this property corresponds to the pruning of values of GAC, when enforced on a CSP previously made kWC. Second, we propose a procedure to enforce DkWC, relying on an encoding of kWC to generate a modified CSP called k-interleaved CSP. Formally, we prove that enforcing GAC on the k-interleaved CSP corresponds to enforcing DkWC on the initial CSP. Consequently, we show that the strong DkWC can be enforced very easily in constraint solvers since the k-interleaved CSP is rather immediate to generate and only existing GAC propagators are required: in a nutshell, DkWC is made as simple and practical as GAC. Our experimental results show the benefits of our approach on a variety of benchmarks.

Generating Random Logic Programs Using Constraint Programming

Testing algorithms across a wide range of problem instances is crucial to ensure the validity of any claim about one algorithm's superiority over another. However, when it comes to inference algorithms for probabilistic logic programs, experimental evaluations are limited to only a few programs. Existing methods to generate random logic programs are limited to propositional programs and often impose stringent syntactic restrictions. We present a novel approach to generating random logic programs and random probabilistic logic programs using constraint programming, introducing a new constraint to control the independence structure of the underlying probability distribution. We also provide a combinatorial argument for the correctness of the model, show how the model scales with parameter values, and use the model to compare probabilistic inference algorithms across a range of synthetic problems. Our model allows inference algorithm developers to evaluate and compare the algorithms across a wide range of instances, providing a detailed picture of their (comparative) strengths and weaknesses.Comment: This is an extended version of the paper published in CP 202

Exploiting short supports for improved encoding of arbitrary constraints into SAT

Encoding to SAT and applying a highly efficient modern SAT solver is an increasingly popular method of solving finite-domain constraint problems. In this paper we study encodings of arbitrary constraints where unit propagation on the encoding provides strong reasoning. Specifically, unit propagation on the encoding simulates generalised arc consistency on the original constraint. To create compact and efficient encodings we use the concept of short support. Short support has been successfully applied to create efficient propagation algorithms for arbitrary constraints. A short support of a constraint is similar to a satisfying tuple however a short support is not required to assign every variable in scope. Some variables are left free to take any value. In some cases a short support representation is smaller than the table of satisfying tuples by an exponential factor. We present two encodings based on short supports and evaluate them on a set of benchmark problems, demonstrating a substantial improvement over the state of the art

Constraint Solving on Hybrid Systems

Applying parallelism to constraint solving seems a promising approach and it has been done with varying degrees of success. Early attempts to parallelize constraint propagation, which constitutes the core of traditional interleaved propagation and search constraint solving, were hindered by its essentially sequential nature. Recently, parallelization efforts have focussed mainly on the search part of constraint solving, as well as on local-search based solving. Lately, a particular source of parallelism has become pervasive, in the guise of GPUs, able to run thousands of parallel threads, and they have naturally drawn the attention of researchers in parallel constraint solving. In this paper, we address challenges faced when using multiple devices for constraint solving, especially GPUs, such as deciding on the appropriate level of parallelism to employ, load balancing and inter-device communication, and present our current solutions

Sliced Table Constraints: Combining Compression and Tabular Reduction

Abstract. Many industrial applications require the use of table constraints (e.g., in configuration problems), sometimes of significant size. During the recent years, researchers have focused on reducing space and time complexities of this type of constraint. Static and dynamic reduction based approaches have been proposed giving new compact representations of table constraints and effective filtering algorithms. In this paper, we study the possibility of combining both static and dynamic reduction techniques by proposing a new compressed form of table constraints based on frequent pattern detection, and exploiting it in STR (Simple Tabular Reduction)