Maximum gradient embeddings and monotone clustering

Manor Mendel, Assaf Naor

Research output: Contribution to journalArticle

Abstract

Let (X,d X) be an n-point metric space. We show that there exists a distribution D over non-contractive embeddings into trees f: X → T such that for every x ∈ X, → where C is a universal constant. Conversely we show that the above quadratic dependence on log n cannot be improved in general. Such embeddings, which we call maximum gradient embeddings, yield a framework for the design of approximation algorithms for a wide range of clustering problems with monotone costs, including fault-tolerant versions of k-median and facility location.

Original languageEnglish (US)
Pages (from-to)581-615
Number of pages35
JournalCombinatorica
Volume30
Issue number5
DOIs
StatePublished - Sep 2010

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Facility Location
Approximation algorithms
Fault-tolerant
Metric space
Approximation Algorithms
Monotone
Clustering
Gradient
Costs
Range of data
Framework
Design

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Computational Mathematics

Cite this

Maximum gradient embeddings and monotone clustering. / Mendel, Manor; Naor, Assaf.

In: Combinatorica, Vol. 30, No. 5, 09.2010, p. 581-615.

Research output: Contribution to journalArticle

Mendel, Manor ; Naor, Assaf. / Maximum gradient embeddings and monotone clustering. In: Combinatorica. 2010 ; Vol. 30, No. 5. pp. 581-615.
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