Computing the Greedy Spanner in Near-Quadratic Time

Authors:
Prosenjit Bose;Paz Carmi;Mohammad Farshi;Anil Maheshwari;Michiel Smid
Affiliations:
School of Computer Science, Carleton University, Ottawa, Canada K1S 5B6;School of Computer Science, Carleton University, Ottawa, Canada K1S 5B6;School of Computer Science, Carleton University, Ottawa, Canada K1S 5B6;School of Computer Science, Carleton University, Ottawa, Canada K1S 5B6;School of Computer Science, Carleton University, Ottawa, Canada K1S 5B6
Venue:
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Year:
2008

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Abstract

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 npoints from a metric space with bounded doubling dimension in time using space. Since the lower bound for computing such spanners is 茂戮驴(n2), the time complexity of our algorithm is optimal to within a logarithmic factor.