Robust geometric spanners

Authors:
Prosenjit Bose;Vida Dujmović;Pat Morin;Michiel Smid
Affiliations:
Carleton University, Ottawa, ON, Canada;Carleton University, Ottawa, ON, Canada;Carleton University, Ottawa, ON, Canada;Carleton University, Ottawa, ON, Canada
Venue:
Proceedings of the twenty-ninth annual symposium on Computational geometry
Year:
2013

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Abstract

Highly connected and yet sparse graphs (such as expanders or graphs of high treewidth) are fundamental, widely a pplicable 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.