Bandwidth and low dimensional embedding

Yair Bartal, Douglas E. Carroll, Adam Meyerson, Ofer Neiman

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We design an algorithm to embed graph metrics into ℓp with dimension and distortion both dependent only upon the bandwidth of the graph. In particular we show that any graph of bandwidth k embeds with distortion polynomial in k into O(log k) dimensional ℓp, 1 ≤ p ≤ ∞. Prior to our result the only known embedding with distortion independent of n was into high dimensional ℓ1 and had distortion exponential in k. Our low dimensional embedding is based on a general method for reducing dimension in an ℓp embedding, satisfying certain conditions, to the intrinsic dimension of the point set, without substantially increasing the distortion. As we observe that the family of graphs with bounded bandwidth are doubling, our result can be viewed as a positive answer to a conjecture of Assouad [2], limited to this family. We also study an extension to graphs of bounded tree-bandwidth.

Original languageEnglish
Title of host publicationApproximation, Randomization, and Combinatorial Optimization
Subtitle of host publicationAlgorithms and Techniques - 14th International Workshop, APPROX 2011 and 15th International Workshop, RANDOM 2011, Proceedings
Pages50-61
Number of pages12
DOIs
StatePublished - 8 Sep 2011
Externally publishedYes
Event14th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2011 and the 15th International Workshop on Randomization and Computation, RANDOM 2011 - Princeton, NJ, United States
Duration: 17 Aug 201119 Aug 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6845 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference14th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2011 and the 15th International Workshop on Randomization and Computation, RANDOM 2011
Country/TerritoryUnited States
CityPrinceton, NJ
Period17/08/1119/08/11

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