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 n points from a metric space with bounded doubling dimension in 
time using 
space. Since the lower bound for computing such spanners is Ω(n
2), the time complexity of our algorithm is optimal to within a logarithmic factor.
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References
Althöfer, I., Das, G., Dobkin, D.P., Joseph, D., Soares, J.: On sparse spanners of weighted graphs. Discrete and Computational Geometry 9(1), 81–100 (1993)
Callahan, P.B., Kosaraju, S.R.: A decomposition of multidimensional point sets with applications to k-nearest-neighbors and n-body potential fields. Journal of the ACM 42, 67–90 (1995)
Chew, L.P.: There is a planar graph almost as good as the complete graph. In: SCG 1986: Proceedings of the 2nd Annual ACM Symposium on Computational Geometry, pp. 169–177 (1986)
Das, G., Narasimhan, G.: A fast algorithm for constructing sparse Euclidean spanners. Int. J. of Computational Geometry & Applications 7, 297–315 (1997)
Farshi, M., Gudmundsson, J.: Experimental study of geometric t-spanners. In: Brodal, G.S., Leonardi, S. (eds.) ESA 2005. LNCS, vol. 3669, pp. 556–567. Springer, Heidelberg (2005)
Farshi, M., Gudmundsson, J.: Experimental study of geometric t-spanners: A running time comparison. In: Demetrescu, C. (ed.) WEA 2007. LNCS, vol. 4525, pp. 270–284. Springer, Heidelberg (2007)
Har-Peled, S.: A simple proof? (2006), http://valis.cs.uiuc.edu/blog/?p=362
Har-Peled, S., Mendel, M.: Fast construction of nets in low-dimensional metrics and their applications. SIAM Journal on Computing 35(5), 1148–1184 (2006)
Keil, J.M., Gutwin, C.A.: Classes of graphs which approximate the complete Euclidean graph. Discrete and Computational Geometry 7, 13–28 (1992)
Narasimhan, G., Smid, M.: Geometric spanner networks. Cambridge University Press, Cambridge (2007)
Peleg, D.: Distributed Computing: A Locality-Sensitive Approach. SIAM, Philadelphia (2000)
Peleg, D., Schäffer, A.: Graph spanners. Journal of Graph Theory 13, 99–116 (1989)
Russel, D., Guibas, L.J.: Exploring protein folding trajectories using geometric spanners. In: Pacific Symposium on Biocomputing, pp. 40–51 (2005)
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Bose, P., Carmi, P., Farshi, M., Maheshwari, A., Smid, M. (2008). Computing the Greedy Spanner in Near-Quadratic Time. In: Gudmundsson, J. (eds) Algorithm Theory – SWAT 2008. SWAT 2008. Lecture Notes in Computer Science, vol 5124. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69903-3_35
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DOI: https://doi.org/10.1007/978-3-540-69903-3_35
Publisher Name: Springer, Berlin, Heidelberg
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