A fast algorithm for constructing sparse Euclidean spanners

Gautam Das, Giri Narasimhan
1994 Proceedings of the tenth annual symposium on Computational geometry - SCG '94  
Gautam Das q t Giri Narasimhanà bstract Let G = (V, 1?) be a n-vertex connected graph with positive edge weights. A subgraph G' is a t-spanner if for all u, v c V, the distance between u and v in the subgraph is at most t times the corresponding distance in G. We design an O(n log2 n) time algorithm which, given a set V of n points in kdimensional space, and any constant t > 1, prduces a t-spanner of the complete Euclidean graph of V. This algorithm retains the spirit of a recent 0(n3 log
more » ... cent 0(n3 log n)-time greedy algorithm which produces tspanners with a small number of edges and a small total edge weight; we use graph clustering techniques to achieve a more efficient implementation. Our ness 1 spanners have similar size and weight sparseaa those constructed by the greedy algorithm. 10th Computational Geometry 94-6/94 Stony Brook, NY, USA
doi:10.1145/177424.177579 dblp:conf/compgeom/DasN94 fatcat:3ro5rv4nabadhhqtgvdkjekdci