Fault-tolerant geometric spanners

Document Type

Conference Proceeding

Publication Date

1-1-2004

Abstract

We present two new results about vertex and edge fault-tolerant spanners in Euclidean spaces. We describe the first construction of vertex and edge fault-tolerant spanners having optimal bounds for maximum degree and total cost. We present a greedy algorithm that for any t > 1 and any non-negative integer k, constructs a k-fault-tolerant t-spanner in which every vertex is of degree O(k) and whose total cost is O(k2) times the cost of the minimum spanning tree; these bounds are asymptotically optimal. Our next contribution is an efficient algorithm for constructing good fault-tolerant spanners. We present a new, sufficient condition for a graph to be a k-fault-tolerant spanner. Using this condition, we design an efficient algorithm that finds fault-tolerant spanners with asymptotically optimal bound for the maximum degree and almost optimal bound for the total cost.

Identifier

4344616177 (Scopus)

Publication Title

Discrete and Computational Geometry

External Full Text Location

https://doi.org/10.1007/s00454-004-1121-7

ISSN

01795376

First Page

207

Last Page

230

Issue

2

Volume

32

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