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.ESA.2020.27
URN: urn:nbn:de:0030-drops-128934
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Buchin, Kevin ; Har-Peled, Sariel ; Oláh, Dániel

Sometimes Reliable Spanners of Almost Linear Size

LIPIcs-ESA-2020-27.pdf (0.6 MB)


Reliable spanners can withstand huge failures, even when a linear number of vertices are deleted from the network. In case of failures, some of the remaining vertices of a reliable spanner may no longer admit the spanner property, but this collateral damage is bounded by a fraction of the size of the attack. It is known that Ω(nlog n) edges are needed to achieve this strong property, where n is the number of vertices in the network, even in one dimension. Constructions of reliable geometric (1+ε)-spanners, for n points in ℝ^d, are known, where the resulting graph has 𝒪(n log n log log⁶n) edges.
Here, we show randomized constructions of smaller size spanners that have the desired reliability property in expectation or with good probability. The new construction is simple, and potentially practical - replacing a hierarchical usage of expanders (which renders the previous constructions impractical) by a simple skip list like construction. This results in a 1-spanner, on the line, that has linear number of edges. Using this, we present a construction of a reliable spanner in ℝ^d with 𝒪(n log log²n log log log n) edges.

BibTeX - Entry

  author =	{Kevin Buchin and Sariel Har-Peled and D{\'a}niel Ol{\'a}h},
  title =	{{Sometimes Reliable Spanners of Almost Linear Size}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{27:1--27:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-162-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{173},
  editor =	{Fabrizio Grandoni and Grzegorz Herman and Peter Sanders},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-128934},
  doi =		{10.4230/LIPIcs.ESA.2020.27},
  annote =	{Keywords: Geometric spanners, vertex failures, reliability}

Keywords: Geometric spanners, vertex failures, reliability
Collection: 28th Annual European Symposium on Algorithms (ESA 2020)
Issue Date: 2020
Date of publication: 26.08.2020

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