It is well known that any non-binary discrete constraint satisfaction problem (CSP) can be translated into an equivalent binary CSP. Two translations are known: the dual graph translation and the hidden variable translation. However, there has been little theoretical or experimental work on how well backtracking algorithms perform on these binary representations in comparison to their performance on the corresponding non-binary CSP. We present both theoretical and empirical results to help understand the tradeoffs involved. In particular, we show that translating a non-binary CSP into a binary representation can be a viable solution technique in certain circumstances. The ultimate aim of this research is to give guidance for when one should consider translating between non-binary and binary representations. Our results supply some initial answers to this question.

The problem of radio frequency assignment is to provide communication channels from limited spectral resources whilst keeping to a minimum the interference suffered by those whishing to communicate in a given radio communication network. This problem is a combinatorial (NP-hard) optimization problem. In 1993, the CELAR (the French "Centre d'Electronique de l'Armement") built a suite of simplified versions of Radio Link Frequency Assignment Problems (RLFAP) starting from data on a real network (Roisnel 93). Initially designed for assessing the performances of several Constraint Logic Programming languages, these benchmarks have been made available to the public in the framework of the European EUCLID project CALMA (Combinatorial Algorithms for Military Applications).

Enforcing local consistencies is one of the main features of constraint reasoning. Which level of local consistency should be used when searching for solutions in a constraint network is a basic question. Arc consistency and partial forms of arc consistency have been widely studied, and have been known for sometime through the forward checking or the MAC search algorithms. Until recently, stronger forms of local consistency remained limited to those that change the structure of the constraint graph, and thus, could not be used in practice, especially on large networks. This paper focuses on the local consistencies that are stronger than arc consistency, without changing the structure of the network, i.e., only removing inconsistent values from the domains. In the last five years, several such local consistencies have been proposed by us or by others. We make an overview of all of them, and highlight some relations between them. We compare them both theoretically and experimentally, considering their pruning efficiency and the time required to enforce them.

. We show that the same methodology used to study phase transition behaviour in NP-complete problems works with a polynomial problem class: establishing arc consistency. A general measure of the constrainedness of an ensemble of problems, used to locate phase transitions in random NP-complete problems, predicts the location of a phase transition in establishing arc consistency. A complexity peak for the AC3 algorithm is associated with this transition. Finite size scaling models both the scaling of this transition and the computational cost. On problems at the phase transition, this model of computational cost agrees with the theoretical worst case. As with NP-complete problems, constrainedness -- and proxies for it which are cheaper to compute -- can be used as a heuristic for reducing the number of checks needed to establish arc consistency in AC3. 1 Introduction Following [4] there has been considerable research into phase transition behaviour in NP-complete problems. Problems from...

We perform a comprehensive theoretical and empirical study of the bene ts of singleton consistencies. Our theoretical results help place singleton consistencies within the hierarchy of local consistencies. To determine the practical value of these theoretical results, we measured the cost-effectiveness of pre-processing with singleton consistency algorithms. Our experiments use both random and structured problems. Whilst pre-processing with singleton consistencies is not in general beneficial for random problems, it starts to pay off when randomness and structure are combined, and it is very worthwhile with structured problems like Golomb rulers. On such problems, pre-processing with consistency techniques as strong as singleton generalized arc-consistency (the singleton extension of generalized arc-consistency) can reduce runtimes. We also show that limiting algorithms that enforce singleton consistencies to a single pass often gives a small reduction in the amount of pruning and improves their cost-effectiveness. These experimental results also demonstrate that conclusions from studies on random problems should be treated with caution.

Singleton arc consistency (SAC) is a local consistency that enhances the pruning capability of arc consistency by ensuring that the network can be made arc consistent after any assignment of a value to a variable. While some algorithms have been proposed in the literature to enforce SAC, a more in-depth theoretical analysis of this local consistency has never been published. In this paper, we give a lower bound to the time complexity of enforcing SAC, and we propose an algorithm that achieves this complexity, thus being optimal. We characterize some properties of SAC which are unusual for a local consistency. Based on some of these properties, we extend SAC to a more powerful local consistency that we compare to the existing local consistencies.

This paper describes a new local search algorithm that provides very high quality solutions to vehicle routing problems. The method uses greedy local search, but avoids local minima by using a large neighbourhood based upon rescheduling selected customer visits using constraint programming techniques. The move operator adopted is completely generic, in that virtually any side constraint can be efficiently incorporated into the search process. Computational results show that a naive implementation of the method produces results bettering the best produced by competing techniques using minima-escaping methods. 1 Introduction In recent years, the method of choice for solving vehicle routing problems has been to use a local search technique. These local search methods have been favoured since they quickly provide solutions to problems of practical size that have not been solved by exact methods. However, because local search techniques only make small changes to the solution, they can onl...

This paper addresses the 3D object recognition problem modelled as a Constraint Satisfaction Problem. In this setting, each object view can be modelled as a constraint graph where nodes are object parts and constraints are topological and geometrical relationships among them. By modelling the problem as a CSP, we can recognize an object when all constraints are satisfied by exploiting results from the CSP field. However, in classical CSPs variable domains have to be statically defined at the beginning of the constraint propagation process. Thus, not only feature acquisition should be completed before the constraint solving process starts, but all image features should be extracted even if not belonging to significant image parts. In visual applications, this requirement turns out to be inefficient since visual features acquisition is a very time consuming task. We present an Interactive Constraint Satisfaction model for problems where variable domains may not be completely known at the beginning of the computation, and can be interactively acquired during the computational process only when needed (on demand). The constraint propagation process works on already known domain values and adds new constraints on unknown domain parts. These new constraints can be used to incrementally process new information without restarting the constraint propagation process from scratch each time new information is available. In addition, these constraints can guide the feature acquisition process, thus focussing attention on significant image parts. We present the Interactive CSP model and a propagation algorithm for it. We propose an implementation of the framework in Constraint Logic Programming on Finite Domains, CLP(FD).

We describe a unified, lazy, declarative framework for solving constraint satisfaction problems, an important subclass of combinatorial search problems. These problems are both practically significant and hard. Finding good solutions involves combining good general-purpose search algorithms with problemspecific heuristics. Conventional imperative algorithms are usually implemented and presented monolithically, which makes them hard to understand and reuse, even though new algorithms often are combinations of simpler ones. Lazy functional languages, such as Haskell, encourage modular structuring of search algorithms by separating the generation and testing of potential solutions into distinct functions communicating through an explicit, lazy intermediate data structure. But only relatively simple search algorithms have been treated in this way in the past. Our framework uses a generic generation and pruning algorithm parameterized by a labeling function that annotates search t...

Constraint Logic Programming languages on Finite Domains, CLP(FD), provide a declarative framework for Artificial Intelligence problems. However, in many real life cases, domains are not known and must be acquired or computed.