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17,049
Searching in metric spaces
, 2001
"... The problem of searching the elements of a set that are close to a given query element under some similarity criterion has a vast number of applications in many branches of computer science, from pattern recognition to textual and multimedia information retrieval. We are interested in the rather gen ..."
Abstract

Cited by 436 (38 self)
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general case where the similarity criterion defines a metric space, instead of the more restricted case of a vector space. Many solutions have been proposed in different areas, in many cases without crossknowledge. Because of this, the same ideas have been reconceived several times, and very different
Gradient flows in metric spaces and in the space of probability measures
 LECTURES IN MATHEMATICS ETH ZÜRICH, BIRKHÄUSER VERLAG
, 2005
"... ..."
Metric spaces
 Formalized Mathematics
, 1990
"... Summary. Sequences in metric spaces are defined. The article contains definitions of bounded, convergent, Cauchy sequences. The subsequences are introduced too. Some theorems concerning sequences are proved. ..."
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Cited by 55 (3 self)
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Summary. Sequences in metric spaces are defined. The article contains definitions of bounded, convergent, Cauchy sequences. The subsequences are introduced too. Some theorems concerning sequences are proved.
Mtree: An Efficient Access Method for Similarity Search in Metric Spaces
, 1997
"... A new access meth d, called Mtree, is proposed to organize and search large data sets from a generic "metric space", i.e. whE4 object proximity is only defined by a distance function satisfyingth positivity, symmetry, and triangle inequality postulates. We detail algorith[ for insertion o ..."
Abstract

Cited by 663 (38 self)
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A new access meth d, called Mtree, is proposed to organize and search large data sets from a generic "metric space", i.e. whE4 object proximity is only defined by a distance function satisfyingth positivity, symmetry, and triangle inequality postulates. We detail algorith[ for insertion
Probabilistic Approximation of Metric Spaces and its Algorithmic Applications
 In 37th Annual Symposium on Foundations of Computer Science
, 1996
"... The goal of approximating metric spaces by more simple metric spaces has led to the notion of graph spanners [PU89, PS89] and to lowdistortion embeddings in lowdimensional spaces [LLR94], having many algorithmic applications. This paper provides a novel technique for the analysis of randomized ..."
Abstract

Cited by 351 (32 self)
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The goal of approximating metric spaces by more simple metric spaces has led to the notion of graph spanners [PU89, PS89] and to lowdistortion embeddings in lowdimensional spaces [LLR94], having many algorithmic applications. This paper provides a novel technique for the analysis of randomized
Metric Space
"... Abstract We consider six selfmaps satisfying the condition of commuting and weak compatibility of mappings and the purpose of this paper is to give some common fixed points theorems for complete multiplicative metric space. ..."
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Abstract We consider six selfmaps satisfying the condition of commuting and weak compatibility of mappings and the purpose of this paper is to give some common fixed points theorems for complete multiplicative metric space.
Metric spaces
"... These slides: available on my web pageExecutive summary Magnitude is a realvalued invariant of metric spaces. It seems not to have been previously investigated. Conjecturally, it captures a great deal of geometric information. It arose from a general study of ‘size ’ in mathematics. Plan 1. Where d ..."
Abstract

Cited by 10 (3 self)
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These slides: available on my web pageExecutive summary Magnitude is a realvalued invariant of metric spaces. It seems not to have been previously investigated. Conjecturally, it captures a great deal of geometric information. It arose from a general study of ‘size ’ in mathematics. Plan 1. Where
Quasimetric and metric spaces
, 2006
"... We give a short review of a construction of Frink to obtain a metric space from a quasimetric space. By an example we illustrate the limits of the construction. 1 ..."
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We give a short review of a construction of Frink to obtain a metric space from a quasimetric space. By an example we illustrate the limits of the construction. 1
Data Structures and Algorithms for Nearest Neighbor Search in General Metric Spaces
, 1993
"... We consider the computational problem of finding nearest neighbors in general metric spaces. Of particular interest are spaces that may not be conveniently embedded or approximated in Euclidian space, or where the dimensionality of a Euclidian representation is very high. Also relevant are highdim ..."
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Cited by 358 (5 self)
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We consider the computational problem of finding nearest neighbors in general metric spaces. Of particular interest are spaces that may not be conveniently embedded or approximated in Euclidian space, or where the dimensionality of a Euclidian representation is very high. Also relevant are high
Results 1  10
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17,049