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Abstract A Top-k retrieval algorithm returns the k best answers of a query according to a given ranking. From a theoretical point of view, the solution of this query is straightforward if we do not take into consideration execution time. However, in many practical situations, execution time is a substantial issue. In such a case, the process of getting the top k in an optimal time becomes an interesting and non-trivial task. This paper presents an algorithm to retrieve the top-k associated to an arbitrary ranking function. The idea is to decompose the ranking function as a supremum of a certain set of functions where an efficient top-k retrieval procedure can be easily applied. Besides the theoretical presentation of the algorithm, the paper provides a set of experiments to validate the approach. [ABSTRACT FROM AUTHOR]

Abstract We propose an alternative to the standard structure of L -fuzzy Mathematical Morphology (MM) by, on the one hand, considering L -fuzzy relations as structuring elements and, on the other hand, by using adjoint triples to handle membership values. Those modifications lead to a framework based on set-theoretical operations where we can prove a representation theorem for algebraic morphological erosions and dilations. In addition, we also present some new results concerning duality and transformation invariance. Concerning duality, we show that duality and adjointness can coexist in this L -fuzzy relational MM. Concerning transformation invariance, we show sufficient conditions to guarantee the invariance of morphological operators under arbitrary transformations. [ABSTRACT FROM AUTHOR]