Given a set V of n points in Rd 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)