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Searching in metric spaces

by Edgar Chávez, Gonzalo Navarro, Ricardo Baeza-yates, José Luis Marroquín , 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) - Add to MetaCart
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 cross-knowledge. 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

by Luigi Ambrosio, Nicola Gigli, et al. - LECTURES IN MATHEMATICS ETH ZÜRICH, BIRKHÄUSER VERLAG , 2005
"... ..."
Abstract - Cited by 457 (45 self) - Add to MetaCart
Abstract not found

Metric spaces

by Stanisława Kanas, Adam Lecko - 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. ..."
Abstract - Cited by 55 (3 self) - Add to MetaCart
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.

M-tree: An Efficient Access Method for Similarity Search in Metric Spaces

by Paolo Ciaccia, Marco Patella, Pavel Zezula , 1997
"... A new access meth d, called M-tree, 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) - Add to MetaCart
A new access meth d, called M-tree, 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

by Yair Bartal - 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 low-distortion embeddings in low-dimensional spaces [LLR94], having many algorithmic applications. This paper provides a novel technique for the analysis of randomized ..."
Abstract - Cited by 351 (32 self) - Add to MetaCart
The goal of approximating metric spaces by more simple metric spaces has led to the notion of graph spanners [PU89, PS89] and to low-distortion embeddings in low-dimensional spaces [LLR94], having many algorithmic applications. This paper provides a novel technique for the analysis of randomized

Metric Space

by Kamal Kumar , Nisha Sharma , Rajeev Jha , Arti Mishra , Manoj Kumar , Kamal Kumar , Nisha Sharma , Rajeev Jha , Arti Mishra , Manoj Kumar , " Weak
"... Abstract We consider six self-maps 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 self-maps 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

by Tom Leinster
"... These slides: available on my web pageExecutive summary Magnitude is a real-valued 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) - Add to MetaCart
These slides: available on my web pageExecutive summary Magnitude is a real-valued 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

Quasi-metric and metric spaces

by Viktor Schroeder , 2006
"... We give a short review of a construction of Frink to obtain a metric space from a quasi-metric 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 quasi-metric space. By an example we illustrate the limits of the construction. 1

Data Structures and Algorithms for Nearest Neighbor Search in General Metric Spaces

by Peter N. Yianilos , 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 high-dim ..."
Abstract - Cited by 358 (5 self) - Add to MetaCart
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

metric spaces

by Duran Turkoglu, Muhib Abuloha, Thabet Abdeljawad , 2008
"... Fixed points of generalized contraction mappings in cone ..."
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Fixed points of generalized contraction mappings in cone
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