License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2019.19
URN: urn:nbn:de:0030-drops-104237
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Buchin, Kevin ; Har-Peled, Sariel ; Oláh, Dániel

A Spanner for the Day After

LIPIcs-SoCG-2019-19.pdf (0.8 MB)


We show how to construct (1+epsilon)-spanner over a set P of n points in R^d that is resilient to a catastrophic failure of nodes. Specifically, for prescribed parameters theta, epsilon in (0,1), the computed spanner G has O(epsilon^{-7d} log^7 epsilon^{-1} * theta^{-6} n log n (log log n)^6) edges. Furthermore, for any k, and any deleted set B subseteq P of k points, the residual graph G \ B is (1+epsilon)-spanner for all the points of P except for (1+theta)k of them. No previous constructions, beyond the trivial clique with O(n^2) edges, were known such that only a tiny additional fraction (i.e., theta) 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.

BibTeX - Entry

  author =	{Kevin Buchin and Sariel Har-Peled and D{\'a}niel Ol{\'a}h},
  title =	{{A Spanner for the Day After}},
  booktitle =	{35th International Symposium on Computational Geometry (SoCG 2019)},
  pages =	{19:1--19:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-104-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{129},
  editor =	{Gill Barequet and Yusu Wang},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-104237},
  doi =		{10.4230/LIPIcs.SoCG.2019.19},
  annote =	{Keywords: Geometric spanners, vertex failures, robustness}

Keywords: Geometric spanners, vertex failures, robustness
Collection: 35th International Symposium on Computational Geometry (SoCG 2019)
Issue Date: 2019
Date of publication: 11.06.2019

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