Improved Algorithms for Constructing Fault-Tolerant Spanners

Let S be a set of n points in a metric space, and k 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 Onlogn + ckn time algorithm that constructs a k-fault-tolerant spanner of degree Ock, whose total edge length is bounded by Ock 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, an algorithm is presented for the Euclidean metric in Rd. This algorithm constructs in Onlogn+k2 n time a k-fault-tolerant spanner with Ok2 n edges.

• Type: Journal
• Year: 2002
• Where: ALGORITHMICA
• Authors: Christos Levcopoulos, Giri Narasimhan, Michiel H. M. Smid
• Keywords: Algorithm, ALGORITHMICA 2002, K-fault-tolerant Spanner, Metric