Light spanners for snowflake metrics

Lee Ad Gottlieb, Shay Solomon

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


A classic result in the study of spanners is the existence of light low-stretch spanners for Euclidean spaces. These spanners have arbitrary low stretch, and weight only a constant factor greater than that of the minimum spanning tree of the points (with dependence on the stretch and Euclidean dimension). A central open problem in this field asks whether other spaces admit low weight spanners as well - for example metric space with low intrinsic dimension - yet only a handful of results of this type are known. In this paper, we consider snowflake metric spaces of low intrinsic dimension. The α-snowflake of a metric (X, δ) is the metric (X, δα), for 0 < α < 1. By utilizing an approach completely different than those used for Euclidean spaces, we demonstrate that snowflake metrics admit light spanners. Further, we show that the spanner is of diameter O(log n), a result not possible for Euclidean spaces. As an immediate corollary to our spanner, we obtain dramatic improvements in algorithms for the traveling salesman problem in this setting, achieving a polynomial-time approximation scheme with near-linear runtime. Along the way, we also show that all ℓp spaces admit light spanners, a result of interest in its own right.

Original languageEnglish
Title of host publicationProceedings of the 30th Annual Symposium on Computational Geometry, SoCG 2014
PublisherAssociation for Computing Machinery
Number of pages9
ISBN (Print)9781450325943
StatePublished - 2014
Externally publishedYes
Event30th Annual Symposium on Computational Geometry, SoCG 2014 - Kyoto, Japan
Duration: 8 Jun 201411 Jun 2014

Publication series

NameProceedings of the Annual Symposium on Computational Geometry


Conference30th Annual Symposium on Computational Geometry, SoCG 2014


  • Metric spanners
  • Snowflake metrics


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