A join-based hybrid parameter for constraint satisfaction

We propose joinwidth, a new complexity parameter for the Constraint Satisfaction Problem (CSP). The definition of joinwidth is based on the arrangement of basic operations on relations (joins, projections, and pruning), which inherently reflects the steps required to solve the instance. We use joinwidth to obtain polynomial-time algorithms (if a corresponding decomposition is provided in the input) as well as fixed-parameter algorithms (if no such decomposition is provided) for solving the CSP. Joinwidth is a hybrid parameter, as it takes both the graphical structure as well as the constraint relations that appear in the instance into account. It has, therefore, the potential to capture larger classes of tractable instances than purely structural parameters like hypertree width and the more general fractional hypertree width (fhtw). Indeed, we show that any class of instances of bounded fhtw also has bounded joinwidth, and that there exist classes of instances of bounded joinwidth and unbounded fhtw, so bounded joinwidth properly generalizes bounded fhtw. We further show that bounded joinwidth also properly generalizes several other known hybrid restrictions, such as fhtw with degree constraints and functional dependencies. In this sense, bounded joinwidth can be seen as a unifying principle that explains the tractability of several seemingly unrelated classes of CSP instances

Tractability in Constraint Satisfaction Problems: A Survey

International audienceEven though the Constraint Satisfaction Problem (CSP) is NP-complete, many tractable classes of CSP instances have been identified. After discussing different forms and uses of tractability, we describe some landmark tractable classes and survey recent theoretical results. Although we concentrate on the classical CSP, we also cover its important extensions to infinite domains and optimisation, as well as #CSP and QCSP

YIELDS: a yet improved limited discrepancy search for CSPs

this paper, we introduce a Yet ImprovEd Limited Discrepancy Search (YIELDS), a complete algorithm for solving constraint satisfaction problems. As indicated in its name, YIELDS is an improved version of limited discrepancy search (LDS). It integrates constraint propagation and variable order learning. The learning scheme, which is the main contribution of this paper, takes benefit from failures encountered during search in order to enhance the efficiency of variable ordering heuristic. As a result, we obtain a search which needs less discrepancies than LDS to find a solution or to state a problem is intractable. This method is then less redundant than LDS. The efficiency of YIELDS is experimentally validated, comparing it with several solving algorithms: depth-bounded discrepancy search, forward checking, and maintaining arc-consistency. Experiments carried out on randomly generated binary CSPs and real problems clearly indicate that YIELDS often outperforms the algorithms with which it is compared, especially for tractable problems.Anglai

Digital in-line particle holography: twin-image suppression using sparse blind source separation

cited By 7International audienceWe propose a robust autofocus method for reconstructing digital holograms and twin-image removal based on blind source separation approach. The method is made up of two components: an efficient quincunx lifting scheme based on wavelet packet transform, whose role is to maximize a sharpness metric related to the sparseness of the input holograms, and a geometric unmixing algorithm, which achieves the separation task. Experimental results confirm the ability of sparse blind source separation to discard the unwanted twin-image from in-line digital holograms of particles. © 2014, Springer-Verlag London

Concurrently Decomposable Constraint Systems

Abstract. In constraint satisfaction, decomposition is a common technique to split a problem in a number of parts in such a way that the global solution can be efficiently assembled from the solutions of the parts. In this paper, we study the decomposition problem from an autonomous agent perspective. Here, a con-straint problem has to be solved by different agents each controlling a disjoint set of variables. Such a problem is called concurrently decomposable if each agent is (i) capable to solve its own part of the problem independently of the others, and (ii) the individual solutions always can be merged to a complete solution of the total problem. First of all, we investigate how difficult it is to decide whether or not a given constraint system and agent partitioning allows for such a concur-rent decomposition. Secondly, we investigate how difficult it is to find suitable reformulations of the original constraint problem that allow for concurrent de-composition.

Directional interchangeability for enhancing CSP solving

This paper introduces directional interchangeability, a weak form of neighborhood interchangeability [Freuder, EC, 1991]. The basic idea is that although two values of a variable may not be neighborhood interchangeable if we consider the whole neighborhood of the variable, they could be neighborhood interchangeable if we restrict the neighborhood to a subset of neighboring variables induced by a variable ordering. In spite of the fact that the proposed concept cannot be used to remove redundant values while preserving problem satisfiability, it provides a mean to partition value domains into subsets of directionally interchangeable values that can be attempted simultaneously by a tree search. Several experiments carried out on various binary CSPs, clearly indicate that variations of the Forward-Checking algorithm and the Maintaining Arc-Consistency algorithm that exploit directional interchangeability often outperform the original algorithms.Anglai

A polynomial relational class of binary CSP

International audienceFinding a solution to a constraint satisfaction problem (CSP) is known to be an NP-hard task. Considerable effort has been spent on identifying tractable classes of CSP,in other words, classes of constraint satisfaction problems for which there are polynomial time recognition and resolution algorithms. In this article, we present a relational tractable class of binary CSP. Our key contribution is a new ternary operation that we name mjx. We first characterize mjx-closed relations which leads to an optimal algorithm to recognize such relations. To reduce space and time complexity, we define a new storage technique for these relations which reduces the complexity of establishing a form of strong directional path consistency, the consistency level that solves all instances of the proposed class (and, indeed, of all relational classes closed under a majority polymorphism)

Blind separation of positive signals by using genetic algorithm

When the source signals are known to be independent, positive and well-grounded which means that they have a non-zero pdf in the region of zero, a few algorithms have been proposed to separate these positive sources. However, in many practical cases, the independent assumption is not always satisfied. In this paper, a new approach is proposed to separate a class of positive sources which are not required to be independent. These source signals can be separated very quickly by using genetic algorithm. The objective function of genetic algorithm is derived from uncorrelated and some special assumptions on such positive source signals. Simulations are employed to illustrate the good performance of our algorithm