A Unified Framework for Light Spanners

Hung Le, Shay Solomon

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

Abstract

Seminal works on light spanners over the years provide spanners with optimal lightness in various graph classes, such as in general graphs, Euclidean spanners, and minor-free graphs. Three shortcomings of previous works on light spanners are: (i) The runtimes of these constructions are almost always sub-optimal, and usually far from optimal. (ii) These constructions are optimal in the standard and crude sense, but not in a refined sense that takes into account a wider range of involved parameters. (iii) The techniques are ad hoc per graph class, and thus can't be applied broadly. This work aims at addressing these shortcomings by presenting a unified framework of light spanners in a variety of graph classes. Informally, the framework boils down to a transformation from sparse spanners to light spanners; since the state-of-the-art for sparse spanners is much more advanced than that for light spanners, such a transformation is powerful. First, we apply our framework to design fast constructions with optimal lightness for several graph classes. Second, we apply our framework to achieve more refined optimality bounds for several graph classes, i.e., the bounds remain optimal when taking into account a wider range of involved parameters, most notably ". Our new constructions are significantly better than the state-of-the-art for every examined graph class.

Original languageEnglish
Title of host publicationSTOC 2023 - Proceedings of the 55th Annual ACM Symposium on Theory of Computing
EditorsBarna Saha, Rocco A. Servedio
Pages295-308
Number of pages14
ISBN (Electronic)9781450399135
DOIs
StatePublished - 2 Jun 2023
Event55th Annual ACM Symposium on Theory of Computing, STOC 2023 - Orlando, United States
Duration: 20 Jun 202323 Jun 2023

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing

Conference

Conference55th Annual ACM Symposium on Theory of Computing, STOC 2023
Country/TerritoryUnited States
CityOrlando
Period20/06/2323/06/23

Keywords

  • Geometric Spanners
  • Graph spanners
  • Light Spanners

All Science Journal Classification (ASJC) codes

  • Software

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