@inproceedings{c7ab51ee462f40cdb9058f6199be3f58,

title = "Metric embedding via shortest path decompositions",

abstract = "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.",

keywords = "Metric embeddings, Normed spaces, Pathwidth, Shortest path decomposition, Treewidth",

author = "Ittai Abraham and Anupam Gupta and Arnold Filtser and Ofer Neiman",

note = "Publisher Copyright: {\textcopyright} 2018 Association for Computing Machinery.; 50th Annual ACM Symposium on Theory of Computing, STOC 2018 ; Conference date: 25-06-2018 Through 29-06-2018",

year = "2018",

month = jun,

day = "20",

doi = "10.1145/3188745.3188808",

language = "English (US)",

series = "Proceedings of the Annual ACM Symposium on Theory of Computing",

publisher = "Association for Computing Machinery",

pages = "912--919",

editor = "Monika Henzinger and David Kempe and Ilias Diakonikolas",

booktitle = "STOC 2018 - Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing",

}