Verification of Item Usage Rules in Product Configuration

In the development of complex products product configuration systems are often used to support the development process. Item Usage Rules (IURs) are conditions for including specific items in products bills of materials based on a high-level product description. Large number of items and significant complexity of IURs make it difficult to maintain and analyze IURs manually. In this paper we present an automated approach for verifying IURs, which guarantees the presence of exactly one item from a predefined set in each product, as well as that an IUR can be reformulated without changing the set of products for which the item was included

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.

Algebraic Properties of Qualitative Spatio-Temporal Calculi

Qualitative spatial and temporal reasoning is based on so-called qualitative calculi. Algebraic properties of these calculi have several implications on reasoning algorithms. But what exactly is a qualitative calculus? And to which extent do the qualitative calculi proposed meet these demands? The literature provides various answers to the first question but only few facts about the second. In this paper we identify the minimal requirements to binary spatio-temporal calculi and we discuss the relevance of the according axioms for representation and reasoning. We also analyze existing qualitative calculi and provide a classification involving different notions of a relation algebra.Comment: COSIT 2013 paper including supplementary materia

On the speed of constraint propagation and the time complexity of arc consistency testing

Establishing arc consistency on two relational structures is one of the most popular heuristics for the constraint satisfaction problem. We aim at determining the time complexity of arc consistency testing. The input structures $G$ and $H$ can be supposed to be connected colored graphs, as the general problem reduces to this particular case. We first observe the upper bound $O(e(G)v(H)+v(G)e(H))$, which implies the bound $O(e(G)e(H))$ in terms of the number of edges and the bound $O((v(G)+v(H))^3)$ in terms of the number of vertices. We then show that both bounds are tight up to a constant factor as long as an arc consistency algorithm is based on constraint propagation (like any algorithm currently known). Our argument for the lower bounds is based on examples of slow constraint propagation. We measure the speed of constraint propagation observed on a pair $G,H$ by the size of a proof, in a natural combinatorial proof system, that Spoiler wins the existential 2-pebble game on $G,H$. The proof size is bounded from below by the game length $D(G,H)$, and a crucial ingredient of our analysis is the existence of $G,H$ with $D(G,H)=\Omega(v(G)v(H))$. We find one such example among old benchmark instances for the arc consistency problem and also suggest a new, different construction.Comment: 19 pages, 5 figure

Domain-Heuristics for Arc-Consistency Algorithms

Arc-consistency algorithms are widely used to prune the search-space of Constraint Satisfaction Problems (CSPs). They use support-checks (also known as consistency-checks) to find out about the properties of CSPs. They use arc-heuristics to select the next constraint and domain-heuristics to select the next values for their next support-check. We will investigate the effects of domain-heuristics by studying the average time-complexity of two arc-consistency algorithms which use different domain-heuristics. We will assume that there are only two variables

Using Images Hierarchies to Understand LANDSAT Images

A.Macewan (ed.