Metric embedding via shortest path decompositions

Ittai Abraham, Anupam Gupta, Arnold Filtser, Ofer Neiman

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

10 Scopus citations


We study the problem of embedding weighted graphs of pathwidth k into ℓp spaces. Our main result is an O(kmin {1/p, 1/2 })-distortion embedding. For p = 1, this is a super-exponential improvement over the best previous bound of Lee and Sidiropoulos. Our distortion bound is asymptotically tight for any fixed p > 1. Our result is obtained via a novel embedding technique that is based on low depth decompositions of a graph via shortest paths. The core new idea is that given a geodesic shortest path P, we can probabilistically embed all points into 2 dimensions with respect to P. For p > 2 our embedding also implies improved distortion on bounded treewidth graphs (O((k log n)1/p)). For asymptotically large p, our results also implies improved distortion on graphs excluding a minor.

Original languageEnglish
Title of host publicationSTOC 2018 - Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing
EditorsMonika Henzinger, David Kempe, Ilias Diakonikolas
PublisherAssociation for Computing Machinery
Number of pages8
ISBN (Electronic)9781450355599
StatePublished - 20 Jun 2018
Event50th Annual ACM Symposium on Theory of Computing, STOC 2018 - Los Angeles, United States
Duration: 25 Jun 201829 Jun 2018

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017


Conference50th Annual ACM Symposium on Theory of Computing, STOC 2018
Country/TerritoryUnited States
CityLos Angeles


  • Metric embeddings
  • Normed spaces
  • Pathwidth
  • Shortest path decomposition
  • Treewidth

ASJC Scopus subject areas

  • Software


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