CONSTRUCTING MULTIDIMENSIONAL SPANNER GRAPHS

Given a connected graph G = (V, E) with positive edge weights, define the distance dG(u, v) between vertices u and v to be the length of a shortest path from u to v in G. A spanning subgraph G' of G is said to be a t-spanner for G if, for every pair of vertices u and v, dG,(u, ti) <= t dG(u, v). Consider a complete graph G whose vertex set is a set of n points in DP and whose edge weights are given by the Lp distance between respective points. Given Input parameter epsilon, 0 < epsilon < 1, we show how to construct a (1 + epsilon)-spanner for G containing O (n/epsilon 2k) edges in O(n log n + n/epsilon 2k) time. We apply this spanner to the construction of approximate minimum spanning trees.