Fast greedy algorithms for constructing sparse geometric spanners

Abstract. Given a set V of n points in R d and a real constant t> 1, we present the first O(n log n)-time algorithm to compute a geometric t-spanner on V. A geometric t-spanner on V is a connected graph G = (V, E) with edge weights equal to the Euclidean distances between the endpoints, and with the property that, for all u, v ∈ V, the distance between u and v in G is at most t times the Euclidean distance between u and v. The spanner output by the algorithm has O(n) edges and weight O(1) · wt(MST), and its degree is bounded by a constant