Abstract

Highly connected and yet sparse graphs (such as expanders or graphs of high treewidth) are fundamental, widely applicable, and extensively studied combinatorial objects. We initiate the study of such highly connected graphs that are, in addition, geometric spanners. We define a property of spanners called robustness. Informally, when one removes a few vertices from a robust spanner, this harms only a small number of other vertices. We show that robust spanners must have a superlinear number of edges, even in one dimension. On the positive side, we give constructions, for any dimension, of robust spanners with a near-linear number of edges.

Keywords

  1. spanners
  2. stretch-factor
  3. spanning-ratio
  4. treewidth
  5. connectivity
  6. expansion

MSC codes

  1. 68M10
  2. 05C10
  3. 65D18

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Information & Authors

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Published In

cover image SIAM Journal on Computing
SIAM Journal on Computing
Pages: 1720 - 1736
ISSN (online): 1095-7111

History

Submitted: 23 April 2012
Accepted: 10 June 2013
Published online: 15 August 2013

Keywords

  1. spanners
  2. stretch-factor
  3. spanning-ratio
  4. treewidth
  5. connectivity
  6. expansion

MSC codes

  1. 68M10
  2. 05C10
  3. 65D18

Authors

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