Many problems in computational sustainability involve constraints on connectivity. When designing a new wildlife corridor, we need it to be geographically connected. When planning the harvest of a forest, we need new areas to harvest to be connected to areas that have already been harvested so we can access them easily. And when town planning, we need to connect new homes to the existing utility infrastructure. To reason about connectivity, we propose a new family of global connectivity constraints. We identify when these constraints can be propagated tractably, and give some efficient, typically linear time propagators for when this is the case. We report results on several benchmark problems which demonstrate the efficiency of our propagation algorithms and the promise offered by reasoning globally about connectivity.

Many natural phenomena exhibit power law spectra. In particular, so-called 1/f α noise series with α close to 1 (also called pink noise) occur in sound, music and countless human artifacts or natural events, from the fluctuations of the flood levels of the Nile to movements of the stock market. As a consequence, many generative models for 1/f noise have been designed to produce series that look or sound “natural” or “human”. In this paper, we formulate the generation of 1/f series as a hard constraint satisfaction problem, so that 1/f noise generation can be used as an add-on to arbitrary sequence generation problems. We take inspiration from a simple yet beautiful stochastic algorithm invented by Voss and introduce the Voss constraint. We show that Voss’ algorithm can be modeled as a tree of ternary sum constraints, leading to efficient filtering. We illustrate our constraint with a melody generation problem, and show that the addition of the Voss constraint tends indeed to produce sequences whose spectrum have a 1/f distribution, regardless of the other constraints of the problem. We discuss the advantages and limitations of this approach and possible extensions.

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.