Light, Reliable Spanners

Arnold Filtser, Yuval Gitlitz, Ofer Neiman

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


A ν-reliable spanner of a metric space (X, d), is a (dominating) graph H, such that for any possible failure set B ⊆ X, there is a set B+ just slightly larger |B+| ≤ (1 + ν) · |B|, and all distances between pairs in X \ B+ are (approximately) preserved in H \ B. Recently, there have been several works on sparse reliable spanners in various settings, but so far, the weight of such spanners has not been analyzed at all. In this work, we initiate the study of light reliable spanners, whose weight is proportional to that of the Minimum Spanning Tree (MST) of X. We first observe that unlike sparsity, the lightness of any deterministic reliable spanner is huge, even for the metric of the simple path graph. Therefore, randomness must be used: an oblivious reliable spanner is a distribution over spanners, and the bound on |B+| holds in expectation. We devise an oblivious ν-reliable (2 + k−21 )-spanner for any k-HST, whose lightness is ≈ ν−2. We demonstrate a matching Ω(ν−2) lower bound on the lightness (for any finite stretch). We also note that any stretch below 2 must incur linear lightness. For general metrics, doubling metrics, and metrics arising from minor-free graphs, we construct light tree covers, in which every tree is a k-HST of low weight. Combining these covers with our results for k-HSTs, we obtain oblivious reliable light spanners for these metric spaces, with nearly optimal parameters. In particular, for doubling metrics we get an oblivious ν-reliable (1 + ε)-spanner with lightness ε−O(ddim) · Õ(ν−2 · log n), which is best possible (up to lower order terms).

Original languageEnglish
Title of host publication40th International Symposium on Computational Geometry, SoCG 2024
EditorsWolfgang Mulzer, Jeff M. Phillips
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959773164
StatePublished - Jun 2024
Event40th International Symposium on Computational Geometry, SoCG 2024 - Athens, Greece
Duration: 11 Jun 202414 Jun 2024

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
ISSN (Print)1868-8969


Conference40th International Symposium on Computational Geometry, SoCG 2024

Bibliographical note

Publisher Copyright:
© Arnold Filtser, Yuval Gitlitz, and Ofer Neiman.


  • HST cover
  • doubling metric
  • light spanner
  • minor free graphs
  • reliable spanner


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