Journal ArticleDOI
On lipschitz embedding of finite metric spaces in Hilbert space
TLDR
In this paper, it was shown that any n point metric space is up to logn lipeomorphic to a subset of Hilbert space, and an example of ann point metric spaces which cannot be embedded in Hilbert space with distortion less than (logn)/(log logn) is given.Abstract:
It is shown that anyn point metric space is up to logn lipeomorphic to a subset of Hilbert space. We also exhibit an example of ann point metric space which cannot be embedded in Hilbert space with distortion less than (logn)/(log logn), showing that the positive result is essentially best possible. The methods used are of probabilistic nature. For instance, to construct our example, we make use of random graphs.read more
Citations
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Journal ArticleDOI
Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions
TL;DR: This work surveys and extends recent research which demonstrates that randomization offers a powerful tool for performing low-rank matrix approximation, and presents a modular framework for constructing randomized algorithms that compute partial matrix decompositions.
Posted Content
Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
TL;DR: In this article, a modular framework for constructing randomized algorithms that compute partial matrix decompositions is presented, which uses random sampling to identify a subspace that captures most of the action of a matrix and then the input matrix is compressed to this subspace, and the reduced matrix is manipulated deterministically to obtain the desired low-rank factorization.
Journal ArticleDOI
Expander graphs and their applications
S Hoory,Nathan Linial +1 more
TL;DR: Expander graphs were first defined by Bassalygo and Pinsker in the early 1970s, and their existence was proved in the late 1970s as discussed by the authors and early 1980s.
Journal ArticleDOI
The geometry of graphs and some of its algorithmic applications
TL;DR: Efficient algorithms for embedding graphs low-dimensionally with a small distortion, and a new deterministic polynomial-time algorithm that finds a (nearly tight) cut meeting this bound.
Journal ArticleDOI
Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
Tom Leighton,Satish Rao +1 more
TL;DR: This paper establishes max-flow min-cut theorems for several important classes of multicommodity flow problems and uses the result to design the first polynomial-time (polylog n-times-optimal) approximation algorithms for well-known NP-hard optimization problems.
References
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Journal ArticleDOI
On type of metric spaces
TL;DR: In this paper, a notion of metric type is introduced and it is shown that for Banach spaces it is consistent with the standard notion of type and a theorem parallel to the Maurey-Pisier Theorem in Local Theory is proved.