In an Artificial Intelligence course, a basic concept is Constraint Satisfaction (CS), which is acknowledged as a hard domain for teachers to teach and student to understand. In this paper, we present a game-based learning approach to assist students in learning CS algorithms, such as arc consistency and search algorithms, for problem solving in an easy, interactive and motivating way. Preliminary valuation has showed promising results.

Constraint programming has become an important technology for solving hard combinatorial problems in a diverse range of application domains. It has its roots in artificial intelligence, mathematical programming, op- erations research, and programming languages. This paper gives a perspective on where constraint programming is today, and discusses a number of opportunities and challenges that could provide focus for the research community into the future.

This paper provides a broad overview of the situation in the area of Parallel Search with a specific focus on Parallel SAT Solving. A set of challenges to researchers is presented which, we believe, must be met to ensure the practical applicability of Parallel SAT Solvers in the future. All these challenges are described informally, but put into perspective with related research results, and a (subjective) grading of difficulty for each of them is provided.

Recent work on planning in incomplete domains focuses on constructing plans that succeed despite incomplete knowledge of action preconditions and effects. As planning models become more expressive, such as in temporal planning, the types of incompleteness may not only change, but plans become more challenging to evaluate. The primary difficulty to temporal plan evaluation is accounting for temporal constraints that may not be satisfied under all interpretations of the incomplete domain. In this work, we formulate incomplete temporal plan evaluation as a generalization of the temporal consistency problem, called partial temporal consistency. We present a knowledge compilation approach that is combined with symbolic constraint propagation and model counting algorithms for counting the number of incomplete domain model interpretations under which a plan is consistent. We present an evaluation that identifies the aspects of incomplete temporal plans most impact performance.

The Word-RAM is a model of computation that takes into account the capacity of a computer to manipulate a word of w bits with a single instruction. Many modern constraint solvers use a bitset data structure to encode the values contained in the variable domains. Using the algorithmic techniques developed for the Word-RAM, we propose new filtering algorithms that can prune Opwq values from a domain in a single instruction. Experiments show that on a processor with w = 64, the new filtering algorithms that enforce domain consis- tency on the constraints A + B = C, |A - B| = C and ALL-DIFFERENT can offer a speed up of a factor 10.

Table constraints are very important in constraint programming as they are present in many real problems from areas such as configuration and databases. As a result, numerous specialized algorithms that achieve generalized arc consistency (GAC) on table constraints have been proposed. Since these algorithms achieve GAC, they operate on one constraint at a time. In this paper we propose an efficient algorithm for table constraints that achieves a stronger local consistency than GAC. This algorithm, called maxRPWC+, is based on the local consistency maxRPWC and allows the efficient handling of intersecting table constraints. Experimental results from benchmark problems demonstrate that maxRPWC+ is clearly more robust than a state-of-the-art GAC algorithm in classes of problems with interleaved table constraints, being orders of magnitude faster in some of these classes.

The Upper Confidence Bounds (UCB) algorithm is a well-known near-optimal strategy for the stochastic multi-armed bandit problem. Its extensions to trees, such as the Upper Confidence Tree (UCT) algorithm, have resulted in good solutions to the problem of Go. This paper introduces DUCT, a distributed algorithm inspired by UCT, for solving Distributed Constraint Optimization Problems (DCOP). Bounds on the solution quality are provided, and experiments show that, compared to existing DCOP approaches, DUCT is able to solve very large problems much more efficiently, or to find significantly higher quality solutions.

Recently a logic programming language AC was proposed by Mellarkod et al. (2008) to integrate answer set programming (ASP) and constraint logic programming. Similarly, Gebser et al. (2009) proposed a CLINGCON language integrating ASP and finite domain constraints. These languages allow new efficient inference algorithms that combine traditional ASP procedures and other methods in constraint programming. In this paper we show that a transition system introduced by Nieuwenhuis et al. (2006) to model SAT solvers can be extended to model the "hybrid" Acsolver algorithm by Mellarkod et al. developed for simple AC programs and the Clingcon algorithm by Gebser et al. for clingcon programs. We define weakly-simple programs and show how the introduced transition systems generalize the Acsolver and Clingcon algorithms to such programs. Finally, we state the precise relation between AC and CLINGCON languages and the Acsolver and Clingcon algorithms.

In maintaining consistencies, such as GAC*, FDGAC* and weak EDGAC*, for global cost functions, Weighted CSP (WCSP) solvers rely on the projection and extension operations, which entail the computation of the cost functions' minima.  Tractability of this minimum computation is essential for efficient execution. Since projections/extensions modify the cost functions, an important issue is tractable projection-safety , concerning whether minimum cost computation remains tractable after projections/extensions. In this paper, we prove that tractable projection-safety is always possible for projections/extensions to/from the nullary cost function ( W 0 ), and always impossible for projections/extensions to/from n -ary cost functions for n > = 2.  When n = 1, the answer is indefinite.  We give a simple negative example, while Lee and Leung's flow-based projection-safe cost functions are also tractable projection-safe. We propose polynomially decomposable cost functions, which are amenable to tractable minimum computation.  We further prove that the polynomial decomposability property is unaffected by projections/extensionsto/from unary cost functions.  Thus, polynomially decomposable cost functions are tractable projection-safe.  We show that the SOFT_AMONG, SOFT_REGULAR, SOFT_GRAMMAR and MAX_WEIGHT/MIN_WEIGHT are polynomially decomposable.  They are embedded in a WCSP solver for extensive experiments to confirm the feasibility and efficiency of our proposal.

In recent years, significant progress in the area of search, constraint satisfaction, and automated reasoning has been driven in part by the study of challenge problems from combinatorics and finite algebra. This work has led to the discovery of interesting discrete structures with intricate mathematical properties. While some of those results have resolved open questions and conjectures, a shortcoming is that they generally do not provide further mathematical insights, from which one could derive more general observations. We propose an approach that integrates specialized combinatorial search, using so-called streamlining, with a human computation component. We use this approach to discover efficient constructive procedures for generating certain classes of combinatorial objects of any size. More specifically, using our framework, we discovered two complementary efficient constructions for generating so-called Spatially Balanced Latin squares (SBLS) of any order N, such that 2N+1 is prime. Previously constructions for SBLSs were not known. Our approach also enabled us to derive a new lower bound for so-called weak Schur numbers, improving on a series of earlier results for Schur numbers.