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Abstract. In 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.

Blind source separation (BSS) consists in processing a set of observed mixed signals to separate them into a set of original components. Most of the current blind separation methods assumes that the source signals are "as statistically independent as possible". In many real-world cases, however, source signals are considerably dependent. In order to cope with such signals, we proposed in [1] a geometric method that separates dependent signals provided that they are nonnegative and locally orthogonal. This paper also presents a geometric method for separating nonnegative source signals which relies on an assumption weaker than local orthogonality. The separation problem relies on the identification of relevant facets of the data cone. After a rigorous proof of the proposed method, we give the details of the separation algorithm and report experiments carried out on signals from various origins, clearly showing the contribution of our method.

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