Computing the Greedy Spanner in Near-Quadratic Time

It is well-known that the greedy algorithm produces high quality spanners and therefore is used in several applications. However, for points in d-dimensional Euclidean space, the greedy algorithm has cubic running time. In this paper we present an algorithm that computes the greedy spanner (spanner computed by the greedy algorithm) for a set of n points from a metric space with bounded doubling dimension in O(n2 log n) time using O(n2 ) space. Since the lower bound for computing such spanners is (n2 ), the time complexity of our algorithm is optimal to within a logarithmic factor.

• Type: Journal
• Year: 2010
• Where: ALGORITHMICA
• Authors: Prosenjit Bose, Paz Carmi, Mohammad Farshi, Anil Maheshwari, Michiel H. M. Smid
• Keywords: ALGORITHMICA 2010, D-dimensional Euclidean Space, Greedy Algorithm, Greedy Spanner