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Improved algorithms for constructing fault-tolerant spanners

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Author

Summary, in English

Let S be a set of n points in a metric space, and let k be a positive integer. Algorithms are given that construct k-fault-tolerant spanners for S. If in such a spanner at most k vertices and/or edges are removed, then each pair of points in the remaining graph is still connected by a "short" path. First, an algorithm is given that transforms an arbitrary spanner into a k-fault-tolerant spanner. For the Euclidean metric in Rd, this leads to an O (n log n + c(k) n)-time algorithm that constructs a k-fault-tolerant spanner of degree O(c(k)), whose total edge length is O(c(k)) times the weight of a minimum spanning tree of S, for some constant c. For constant values of k, this result is optimal, In the second part of the paper, algorithms are presented for the Euclidean metric in Rd. These algorithms construct (i) in O(n log n + k(2)n) time, a k-fault-tolerant spanner with O (k(2)n) edges, and (ii) in O(kn log n) time, such a spanner with O(kn log n) edges.

Department/s

  • Computer Science

Publishing year

2002

Language

English

Pages

144-156

Publication/Series

Algorithmica

Volume

32

Issue

1

Document type

Journal article

Publisher

Springer

Topic

  • Computer Science

Keywords

  • well-separated pairs
  • fault-tolerance
  • computational geometry
  • spanners

Status

Published

ISBN/ISSN/Other

  • ISSN: 0178-4617