Four problems of proximity between two convex polytopes in R' are considered. The convex polytopes are represented as convex hulls of finite sets of points. Let the total number of points in the two finite sets be n. W e show that three of the proximity problems, viz., checking intersection, checking whether the polytopes are just touching and finding the distance between them, can be solved in...

The paper deals with the registration and modeling of multiple 3-D proole maps acquired from diierent viewpoints by light striping. We analyze the propagation of measurement and calibration errors to the registration parameters and further to the reconstructed model of the scene consisting of planar patches. The analysis is performed for two strategies. In the rst strategy, the maps are registe...

Proximity searching consists in retrieving the most similar objects to a given query. This kind of searching is a basic tool in many fields of artificial intelligence, because it can be used as a search engine to solve problems like kNN searching. A common technique to solve proximity queries is to use an index. In this paper, we show a variant of the permutation based index, which, in his orig...

This paper proposes a method of ranking XML documents with respect to an Information Retrieval query by means of fuzzy logic. The proposed method allows imprecise queries to be evaluated against an XML document collection and it provides a model of ranking XML documents. In addition the proposed method enables sophisticated ranking of documents by employing proximity measures and the concept of...

The main bottleneck of the research in metric space searching is the so-called curse of dimensionality, which makes the task of searching some metric spaces intrinsically diicult, whatever algorithm is used. A recent trend to break this bottleneck resorts to probabilistic algorithms , where it has been shown that one can nd 99% of the elements at a fraction of the cost of the exact algorithm. T...

We develop an intuitive geometric interpretation of the standard support vector machine (SVM) for classification of both linearly separable and inseparable data and provide a rigorous derivation of the concepts behind the geometry. For the separable case finding the maximum margin between the two sets is equivalent to finding the closest points in the smallest convex sets that contain each clas...

In this paper we investigate the effects of replacing the objective function of a 0-1 Mixed-Integer Convex Program (MIP) with a “proximity” one, with the aim of enhancing the heuristic behavior of a black-box solver. The relationship of this approach with primal integer methods is also addressed. Promising computational results on different proof-of-concept implementations are presented, sugges...

Berinde [V. Berinde, Approximating fixed points of weak contractions using the Picard iteration, Nonlinear Anal. Forum {bf 9} (2004), 43-53] introduced almost contraction mappings and proved Banach contraction principle for such mappings. The aim of this paper is to introduce the notion of multivalued almost $Theta$- contraction mappings andto prove some best proximity point results for t...

A characterization of the quotient proximity is given. It is used to find necessary and sufficient conditions for every proximity map on a space to be a topological quotient map. It is shown that a separated proximity space is compact iff every /7-map on X with separated range is a proximity quotient map. Introduction. In 1959 Katetov [3] introduced proximity quotient maps. They have since been...