On low dimensional local embeddings

Ittai Abraham, Yair Bartal, Ofer Neiman

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

7 Scopus citations

Abstract

We study the problem of embedding metric spaces into low dimensional ℓp spaces while faithfully preserving distances from each point to its k nearest neighbors. We show that any metric space can be embedded into ℓpO(ep log2 k) with k-local distortion of O((log k)/p). We also show that any ultrametric can be embedded into ℓpO(log k)/c3 with k-local distortion 1 + ∈. Our embedding results have immediate applications to local Distance Oracles. We show how to preprocess a graph in polynomial time to obtain a data structure of O(nk1/t log2 k) bits, such that distance queries from any node to its k nearest neighbors can be answered with stretch O(t).

Original languageEnglish
Title of host publicationProceedings of the 20th Annual ACM-SIAM Symposium on Discrete Algorithms
PublisherAssociation for Computing Machinery (ACM)
Pages875-884
Number of pages10
ISBN (Print)9780898716801
DOIs
StatePublished - 1 Jan 2009
Externally publishedYes
Event20th Annual ACM-SIAM Symposium on Discrete Algorithms - New York, NY, United States
Duration: 4 Jan 20096 Jan 2009

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Conference

Conference20th Annual ACM-SIAM Symposium on Discrete Algorithms
Country/TerritoryUnited States
CityNew York, NY
Period4/01/096/01/09

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