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Efficient Construction of a Bounded Degree Spanner with Low Weight
 

Summary: Efficient Construction of a Bounded Degree Spanner
with Low Weight
Sunil Arya
Michiel Smid
Abstract
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 con-

  

Source: Arya, Sunil - Department of Computer Science, Hong Kong University of Science and Technology

 

Collections: Computer Technologies and Information Sciences