Improved Greedy Algorithms for Constructing Sparse Geometric Spanners

Abstract

Let G=(V, E) be a connected graph with positive weights and n vertices. A subgraph G is a t-spanner if for all u, v∈V , the distance between u and v in the subgraph G is at most t times the corresponding distance in G. We show a O(n log n)-time algorithm which, given a set V of n points in d-dimensional space, and any constant t>1, produces a t-spanner of the complete Euclidean graph of G. The produced spanner have O(n) edges, constant degree and weight O(wt(MST)).