You may skip most of these readings if you have prior programming experience in Java.

Welcome to the On-Line Guide to CONSTRAINT PROGRAMMING designed and maintained by Roman Barták. I have opened this site as an on-line tutorial or, if you want, a textbook for beginners to the area of constraint programming. This area belongs to the less known software technologies but it rapidly evolves and brings a significant commercial interest.

Description: Constraint satisfaction problems (CSPs) are pervasive in AI problems. A constraint satisfaction problem is the problem of assigning values to variables that satisfy some constraints. This constraint satisfaction problem solver (arc consistency) tool is designed to help you learn about solving CSPs with a systematic search technique called arc consistency.

The development of problem solvers for configuration tasks is one of the most successful and mature application areas of artificial intelligence. The provision of tailored products, services, and systems requires efficient engineering and design processes where configurators play a crucial role. Because one of the core competencies of Siemens is to provide such highly engineered and customized systems, ranging from solutions for medium-sized and small businesses up to huge industrial plants, the efficient implementation and maintenance of configurators are important goals for the success of many departments. For more than 25 years the application of constraint-based methods has proven to be a key technology in order to realize configurators at Siemens. This article summarizes the main aspects and insights we have gained looking back over this period. In particular, we highlight the main technology factors regarding knowledge representation, reasoning, and integration which were important for our achievement. Finally we describe selected key application areas where the business success vitally depends on the high productivity of configuration processes.

We study probability measures induced by set functions with constraints. Such measures arise in a variety of real-world settings, where prior knowledge, resource limitations, or other pragmatic considerations impose constraints. We consider the task of rapidly sampling from such constrained measures, and develop fast Markov chain samplers for them. Our first main result is for MCMC sampling from Strongly Rayleigh (SR) measures, for which we present sharp polynomial bounds on the mixing time. As a corollary, this result yields a fast mixing sampler for Determinantal Point Processes (DPPs), yielding (to our knowledge) the first provably fast MCMC sampler for DPPs since their inception over four decades ago. Beyond SR measures, we develop MCMC samplers for probabilistic models with hard constraints and identify sufficient conditions under which their chains mix rapidly. We illustrate our claims by empirically verifying the dependence of mixing times on the key factors governing our theoretical bounds.

The constraint satisfaction problem (CSP) involves deciding, given a set of variables and a set of constraints on the variables, whether or not there is an assignment to the variables satisfying all of the constraints. One formulation of the CSP is as the problem of deciding, given a pair (G,H) of relational structures, whether or not there is a homomorphism from the first structure to the second structure. The CSP is in general NP-hard; a common way to restrict this problem is to fix the second structure H, so that each structure H gives rise to a problem CSP(H). The problem family CSP(H) has been studied using an algebraic approach, which links the algorithmic and complexity properties of each problem CSP(H) to a set of operations, the so-called polymorphisms of H. Certain types of polymorphisms are known to imply the polynomial-time tractability of $CSP(H)$, and others are conjectured to do so. This article systematically studies---for various classes of polymorphisms---the computational complexity of deciding whether or not a given structure H admits a polymorphism from the class. Among other results, we prove the NP-completeness of deciding a condition conjectured to characterize the tractable problems CSP(H), as well as the NP-completeness of deciding if CSP(H) has bounded width.

We study probability measures induced by set functions with constraints. Such measures arise in a variety of real-world settings, where prior knowledge, resource limitations, or other pragmatic considerations impose constraints. We consider the task of rapidly sampling from such constrained measures, and develop fast Markov chain samplers for them. Our first main result is for MCMC sampling from Strongly Rayleigh (SR) measures, for which we present sharp polynomial bounds on the mixing time. As a corollary, this result yields a fast mixing sampler for Determinantal Point Processes (DPPs), yielding (to our knowledge) the first provably fast MCMC sampler for DPPs since their inception over four decades ago. Beyond SR measures, we develop MCMC samplers for probabilistic models with hard constraints and identify sufficient conditions under which their chains mix rapidly. We illustrate our claims by empirically verifying the dependence of mixing times on the key factors governing our theoretical bounds.

Inference in Markov random fields subject to consistency structure is a fundamental problem that arises in many real-life applications. In order to enforce consistency, classical approaches utilize consistency potentials or encode constraints over feasible instances. Unfortunately this comes at the price of a serious computational bottleneck. In this paper we suggest to tackle consistency by incorporating constraints on beliefs. This permits derivation of a closed-form message-passing algorithm which we refer to as the Constraints Based Convex Belief Propagation (CBCBP). Experiments show that CBCBP outperforms the standard approach while being at least an order of magnitude faster.

Towards learning programs from data, we introduce the problem of sampling programs from posterior distributions conditioned on that data. Within this setting, we propose an algorithm that uses a symbolic solver to efficiently sample programs. The proposal combines constraint-based program synthesis with sampling via random parity constraints. We give theoretical guarantees on how well the samples approximate the true posterior, and have empirical results showing the algorithm is efficient in practice, evaluating our approach on 22 program learning problems in the domains of text editing and computer-aided programming.

Distributed constraint optimization problems enable the representation of many combinatorial problems that are distributed by nature. An important motivation for such problems is to preserve the privacy of the participating agents during the solving process. The present paper introduces a novel privacy-preserving branch and bound algorithm for this purpose. The proposed algorithm, P-SyncBB, preserves constraint, topology and decision privacy. The algorithm requires secure solutions to several multi-party computation problems. Consequently, appropriate novel secure protocols are devised and analyzed. An extensive experimental evaluation on different benchmarks, problem sizes, and constraint densities shows that P-SyncBB exhibits superior performance to other privacy-preserving complete DCOP algorithms.