Fast Greedy Algorithms for Constructing Sparse Geometric Spanners

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)

• Type: Journal
• Year: 2002
• Where: SIAMCOMP
• Authors: Joachim Gudmundsson, Christos Levcopoulos, Giri Narasimhan
• Keywords: Algorithm, Connected Graph, Geometric T-spanner, SIAMCOMP 2002