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ESA
1994
Springer

Efficient Construction of a Bounded Degree Spanner with Low Weight

10 years 2 months ago
Efficient Construction of a Bounded Degree Spanner with Low Weight
Let S be a set of n points in IRd and let t > 1 be a real number. A t-spanner for S is a graph having the points of S as its vertices such that for any pair p, q of points there is a path between them of length at most t times the Euclidean distance between p and q. An efficient implementation of a greedy algorithm is given that constructs a t-spanner having bounded degree such that the total length of all its edges is bounded by O(log n) times the length of a minimum spanning tree for S. The algorithm has running time O(n logd n). Applying recent results of Das, Narasimhan and Salowe to this t-spanner gives an O(n logd n) time algorithm for constructing a t-spanner having bounded degree and whose total edge length is proportional to the length of a minimum spanning tree for S. Previously, no o(n2) time algorithms were known for constructing a t-spanner of bounded degree. In the final part of the paper, an application to the problem of distance enumeration is given.
Sunil Arya, Michiel H. M. Smid
Added 09 Aug 2010
Updated 09 Aug 2010
Type Conference
Year 1994
Where ESA
Authors Sunil Arya, Michiel H. M. Smid
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