A spanner for the day after

Kevin Buchin, Sariel Har-Peled, Dániel Oláh

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

4 Citations (Scopus)
20 Downloads (Pure)


We show how to construct (1 + ε)-spanner over a set P of n points in ℝd that is resilient to a catastrophic failure of nodes. Specifically, for prescribed parameters ϑ, ε ∈ (0, 1), the computed spanner G has O(ε−7d log7 ε−1 · ϑ−6n log n(log log n)6) edges. Furthermore, for any k, and any deleted set B ⊆ P of k points, the residual graph G \ B is (1 + ε)-spanner for all the points of P except for (1 + ϑ)k of them. No previous constructions, beyond the trivial clique with O(n2) edges, were known such that only a tiny additional fraction (i.e., ϑ) lose their distance preserving connectivity. Our construction works by first solving the exact problem in one dimension, and then showing a surprisingly simple and elegant construction in higher dimensions, that uses the one dimensional construction in a black box fashion.

Original languageEnglish
Title of host publication35th International Symposium on Computational Geometry, SoCG 2019
EditorsGill Barequet, Yusu Wang
PublisherSchloss Dagstuhl - Leibniz-Zentrum für Informatik
Number of pages15
ISBN (Electronic)9783959771047
Publication statusPublished - 1 Jun 2019
Event35th International Symposium on Computational Geometry, (SoCG2019) - Portland, United States
Duration: 18 Jun 201921 Jun 2019

Publication series

NameLeibniz International Proceedings in Informatics (LIPIcs)


Conference35th International Symposium on Computational Geometry, (SoCG2019)
Abbreviated titleSoCG2019
Country/TerritoryUnited States
Internet address


  • Geometric spanners
  • Robustness
  • Vertex failures

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