The binary Constraint Satisfaction Problem (CSP) is to decide whether there exists an assignment to a set of variables which satisfies specified constraints between pairs of variables. A CSP instance can be presented as a labelled graph (called the microstructure) encoding both the forms of the constraints and where they are imposed. We consider subproblems defined by restricting the allowed form of the microstructure. One form of restriction that has previously been considered is to forbid certain specified substructures (patterns). This captures some tractable classes of the CSP, but does not capture the well-known property of acyclicity. In this paper we introduce the notion of a topological minor of a binary CSP instance. By forbidding certain patterns as topological minors we obtain a compact mechanism for expressing several novel tractable classes, including new generalisations of the class of acyclic instances.

This work compares two actions' concurrency and co-occurrence employed in temporal modeling languages, one with a PDDL-style action modeling languages used by the AI planning community, exclusion mechanism, and another with an explicit and argue that they explain why MILP or SMT have notion of resources, and investigates their seemed unattractive. Specifically, we observe that PDDL 2.1 implications on constraint-based search. The first [Fox and Long, 2003] induces temporal gaps between consecutive mechanism forces temporal gaps in action schedules interdependent actions, and these gaps often induce and have a high performance penalty. The second twice the number of steps in the plans than what is necessary, mechanism avoids the gaps, with dramatically with strong negative performance implications. The gaps are improved performance.

Raven’s Progressive Matrices (RPMs) are a popular family of general intelligence tests, and provide a non-verbal measure of a test subject’s reasoning abilities. Traditionally RPMs have been manually designed. To make them readily available for both practice and examination, we tackle the problem of automatically synthesizing RPMs. Our goal is to efficiently generate a large number of RPMs that are authentic (i.e. similar to manually written problems), interesting (i.e. diverse in terms of difficulty), and well-formed (i.e unambiguous). The main technical challenges are: How to formalize RPMs to accommodate their seemingly enormous diversity, and how to define and enforce their validity? To this end, we (1) introduce an abstract representation of RPMs using first-order logic, and (2) restrict instantiations to only valid RPMs. We have realized our approach and evaluated its efficiency and effectiveness. We show that our system can generate hundreds of valid problems per second with varying levels of difficulty. More importantly, we show, via a user study with 24 participants, that the generated problems are statistically indistinguishable from actual problems. This work is an exciting instance of how logic and reasoning may aid general learning.

We study the adjustment and use of the Max-sumalgorithm for solving Asymmetric Distributed ConstraintOptimization Problems (ADCOPs). First, we formalize asymmetric factor-graphs and apply the different versions of Max-sum to them. Apparently, in contrast to local search algorithms, most Max-sum versions perform similarly when solving symmetric and asymmetric problems and some even perform better on asymmetric problems. Second, we prove that the convergence properties of Max-sum ADVP (an algorithm that was previously found to outperform other Max-sum versions) and the quality of the solutions it produces are dependent on the order between nodes involved in each constraint, i.e., the inner constraint order (ICO). A standard ICO allows to reproduce the properties achieved for symmetric problems, and outperform previously proposed local search ADCOP algorithms. Third, we demonstrate that a non-standard ICO can be used to balance exploration and exploitation, resulting in the best performing Max-sum version on both symmetric and asymmetric standard benchmarks.

As part of the ongoing effort of designing secure DCOP algorithms, we propose P-Max-Sum, the first private algorithm that is based on Max-Sum. The proposed algorithm has multiple agents preforming the role of each node in the factor graph, on which the Max-Sum algorithm operates. P-Max-Sum preserves three types of privacy: topology privacy, constraint privacy, and assignment/decision privacy.By allowing a single call to a trusted coordinator, P-Max-Sum also preserves agent privacy. The two main cryptographic means that enable this privacy preservation are secret sharing and homomorphic encryption. Our experiments on structured and realistic problems show that the overhead of privacy preservation in terms of runtime is reasonable.

Distributed constraint optimization (DCOP) is an important framework for coordinated multiagent decision making. We address a practically useful variant of DCOP, called resource-constrained DCOP (RC-DCOP), which takes into account agents' consumption of shared limited resources. We present a promising new class of algorithm for RC-DCOPs by translating the underlying coordination problem to probabilistic inference. Using inference techniques such as expectation-maximization and convex optimization machinery, we develop a novel convergent message-passing algorithm for RC-DCOPs. Experiments on standard benchmarks show that our approach provides better quality than previous best DCOP algorithms and has much lower failure rate. Comparisons against an efficient centralized solver show that our approach provides near-optimal solutions, and is significantly faster on larger instances.

We increase the usefulness of Chu and Stuckey's work by automating it, that is, by developing a method to (a) automatically The exploitation of dominance relations in constraint identify symmetries for a given problem, and (b) optimization problems can lead to dramatic automatically construct the associated dominance breaking reductions in search space. We propose an automatic constraints. Note that these dominance breaking constraints method to detect some of the dominance relations are not symmetry breaking constraints, as the key element manually identified by Chu and Stuckey for is for f(σ(θ)) to be better. Further, the symmetries need to optimization problems, and to construct the associated be detected for the inherent satisfaction problem -- that is, dominance breaking constraints. Experimental the problem without the objective function -- or, otherwise, results show that the method is able to find several f(σ(θ)) will be equal to f(θ), not better.

Generalized arc consistency (GAC) is one of the most fundamental properties for reducing the search space when solving constraint satisfaction problems (CSPs). Consistencies stronger than GAC have also been shown useful, but the challenge is to develop efficient and simple filtering algorithms. Several CSP transformations are proposed recently so that the GAC algorithms can be applied on the transformedCSP to enforce stronger consistencies. Among them, the factor encoding (FE) is shown to be promising with respect to recent higher-order consistency algorithms. Nonetheless, one potential drawback of the FE is the fact that it enlarges the table relations as it increases constraint arity. We propose a variation of the FE that aims at reducing redundant columns in the constraints of the FE while still preserving full pairwise consistency. Experiments show that the new approach is competitive over a variety of random and structured benchmarks.

Presolving is a preprocessing step performed by optimisation solvers to improve performance. However, these solvers cannot easily exploit high-level model structure as available in modelling languages such as MiniZinc or Essence. We present an integrated approach that performs presolving as a separate pass during the compilation from high-level optimisation models to solver-level programs. The compiler produces a representation of the model that is suitable for presolving by retaining some of the high-level structure. It then uses information learned during presolving to generate the final solver-level representation. Our approach introduces the novel concept of variable paths that identify variables which are common across multiple compilation passes, increasing the amount of shared information. We show that this approach can lead to both faster compilation and more efficient solver-level programs.

The generation and GAC enforcement of a large number of weak nogoods in Symmetry Breaking During Search (SBDS) is costly and often not worthwhile in terms of prunings. In this paper, we propose weak-nogood consistency (WNC) for nogoods and a lazy propagator for SBDS (and its variants) using watched literal technology. We give formal results on the strength and relatively low space and time complexities of the lazy propagator. Nogoods collected for each symmetry are increasing. We further define generalized weak-incNGs consistency (GWIC) for a conjunction of increasing nogoods, and give a lazy propagator for the incNGs global constraint. We prove GWIC on a conjunction is equivalent to WNC on individual nogoods, and give the space and time complexities. Various lazy versions of SBDS and its variants are implemented. We give experimentation to demonstrate the efficiency of the lazy versions as compared to state of the art symmetry breaking methods.