A spanner for the day after

Kevin Buchin, Sariel Har-Peled, Dániel Oláh

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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 (US)
Title of host publication35th International Symposium on Computational Geometry, SoCG 2019
EditorsGill Barequet, Yusu Wang
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771047
StatePublished - Jun 1 2019
Event35th International Symposium on Computational Geometry, SoCG 2019 - Portland, United States
Duration: Jun 18 2019Jun 21 2019

Publication series

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


Conference35th International Symposium on Computational Geometry, SoCG 2019
Country/TerritoryUnited States


  • Geometric spanners
  • Robustness
  • Vertex failures

ASJC Scopus subject areas

  • Software


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