The greedy spanner is existentially optimal: [Extended Abstract]

Arnold Filtser, Shay Solomon

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

32 Scopus citations

Abstract

The greedy spanner is arguably the simplest and most well-studied spanner construction. Experimental results demonstrate that it is at least as good as any other spanner construction, in terms of both the size and weight parameters. However, a rigorous proof for this statement has remained elusive. In this work we fill in the theoretical gap via a surprisingly simple observation: The greedy spanner is existentially optimal (or existentially near-optimal) for several important graph families. Focusing on the weight parameter, the state-of-the-art spanner constructions for both general graphs (due to Chechik and Wulff-Nilsen [SODA16]) and doubling metrics (due to Gottlieb [FOCS15]) are complex. Plugging our observation on these results, we conclude that the greedy spanner achieves near-optimal weight guarantees for both general graphs and doubling metrics, thus resolving two longstanding conjectures in the area. Further, we observe that approximate-greedy algorithms are existentially near-optimal as well. Consequently, we provide an O(n log n)-time construction of (1+ϵ)-spanners for doubling metrics with constant lightness and degree. Our construction improves Gottliebs construction, whose runtime is O(n log2 n) and whose number of edges and degree are unbounded, and remarkably, it matches the state-of-the-art Euclidean result (due to Gudmundsson et al. [SICOMP02]) in all the involved parameters (up to dependencies on ϵ and the dimension).

Original languageEnglish
Title of host publicationPODC 2016 - Proceedings of the 2016 ACM Symposium on Principles of Distributed Computing
PublisherAssociation for Computing Machinery
Pages9-17
Number of pages9
ISBN (Electronic)9781450339643
DOIs
StatePublished - 25 Jul 2016
Externally publishedYes
Event35th ACM Symposium on Principles of Distributed Computing, PODC 2016 - Chicago, United States
Duration: 25 Jul 201628 Jul 2016

Publication series

NameProceedings of the Annual ACM Symposium on Principles of Distributed Computing
Volume25-28-July-2016

Conference

Conference35th ACM Symposium on Principles of Distributed Computing, PODC 2016
Country/TerritoryUnited States
CityChicago
Period25/07/1628/07/16

Bibliographical note

Publisher Copyright:
© 2016 ACM.

Keywords

  • Doubling metric
  • Graph spanner
  • Greedy algorithm
  • Greedy spanner
  • Light spanner

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