Maximum gradient embeddings and monotone clustering

Manor Mendel, Assaf Naor

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Let (X, d x) be an n-point metric space. We show that there exists a distribution & over non-contractive embeddings into trees f : X → T such that for every x ∈ X, E D [max v∈X\(x) d T(f(x), f(y))/d X(x, y)] < C(log n) 2 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)
Title of host publicationApproximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings
Pages242-256
Number of pages15
Volume4627 LNCS
StatePublished - 2007
Event10th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2007 and 11th International Workshop on Randomization and Computation, RANDOM 2007 - Princeton, NJ, United States
Duration: Aug 20 2007Aug 22 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4627 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other10th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2007 and 11th International Workshop on Randomization and Computation, RANDOM 2007
CountryUnited States
CityPrinceton, NJ
Period8/20/078/22/07

Fingerprint

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

ASJC Scopus subject areas

  • Computer Science(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Theoretical Computer Science

Cite this

Mendel, M., & Naor, A. (2007). Maximum gradient embeddings and monotone clustering. In Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings (Vol. 4627 LNCS, pp. 242-256). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4627 LNCS).

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

Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings. Vol. 4627 LNCS 2007. p. 242-256 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4627 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Mendel, M & Naor, A 2007, Maximum gradient embeddings and monotone clustering. in Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings. vol. 4627 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4627 LNCS, pp. 242-256, 10th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2007 and 11th International Workshop on Randomization and Computation, RANDOM 2007, Princeton, NJ, United States, 8/20/07.
Mendel M, Naor A. Maximum gradient embeddings and monotone clustering. In Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings. Vol. 4627 LNCS. 2007. p. 242-256. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
Mendel, Manor ; Naor, Assaf. / Maximum gradient embeddings and monotone clustering. Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings. Vol. 4627 LNCS 2007. pp. 242-256 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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