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FOCS
2004
IEEE
14 years 2 months ago
Measured Descent: A New Embedding Method for Finite Metrics
We devise a new embedding technique, which we call measured descent, based on decomposing a metric space locally, at varying speeds, according to the density of some probability m...
Robert Krauthgamer, James R. Lee, Manor Mendel, As...
APPROX
2007
Springer
102views Algorithms» more  APPROX 2007»
14 years 5 months ago
Hardness of Embedding Metric Spaces of Equal Size
Abstract. We study the problem embedding an n-point metric space into another n-point metric space while minimizing distortion. We show that there is no polynomial time algorithm t...
Subhash Khot, Rishi Saket
APPROX
2007
Springer
67views Algorithms» more  APPROX 2007»
14 years 5 months ago
Maximum Gradient Embeddings and Monotone Clustering
abstract Manor Mendel1 and Assaf Naor2 1 The Open University of Israel 2 Courant Institute Let (X, dX ) be an n-point metric space. We show that there exists a distribution D over ...
Manor Mendel, Assaf Naor
STOC
2004
ACM
122views Algorithms» more  STOC 2004»
14 years 11 months ago
Estimating the weight of metric minimum spanning trees in sublinear-time
In this paper we present a sublinear time (1+ )-approximation randomized algorithm to estimate the weight of the minimum spanning tree of an n-point metric space. The running time...
Artur Czumaj, Christian Sohler
STOC
2005
ACM
118views Algorithms» more  STOC 2005»
14 years 11 months ago
Euclidean distortion and the sparsest cut
We prove that every n-point metric space of negative type (and, in particular, every npoint subset of L1) embeds into a Euclidean space with distortion O( log n ? log log n), a r...
Sanjeev Arora, James R. Lee, Assaf Naor