Maximum gradient embeddings and monotone clustering

Manor Mendel; Assaf Naor

doi:10.1007/978-3-540-74208-1_18

Maximum gradient embeddings and monotone clustering

Manor Mendel, Assaf Naor

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English (US)
Title of host publication	Approximation, Randomization, and Combinatorial Optimization
Subtitle of host publication	Algorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings
Publisher	Springer Verlag
Pages	242-256
Number of pages	15
ISBN (Print)	9783540742074
DOIs	https://doi.org/10.1007/978-3-540-74208-1_18
State	Published - 2007
Event	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 Duration: Aug 20 2007 → Aug 22 2007

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	4627 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	10th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2007 and 11th International Workshop on Randomization and Computation, RANDOM 2007
Country/Territory	United States
City	Princeton, NJ
Period	8/20/07 → 8/22/07

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

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10.1007/978-3-540-74208-1_18

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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 (pp. 242-256). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4627 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-540-74208-1_18

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. Springer Verlag, 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 proceeding › Conference 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. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4627 LNCS, Springer Verlag, 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. https://doi.org/10.1007/978-3-540-74208-1_18

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. Springer Verlag. 2007. p. 242-256. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-540-74208-1_18

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. Springer Verlag, 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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Maximum gradient embeddings and monotone clustering

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