Abstract
Let G=(V,E) be a connected graph with positive weights and n vertices. A subgraph G′ is a t-spanner if for all u, v∈V, the distance between u and v in the subgraph G′ is at most t times the corresponding distance in G. We show a O(nlogn)-time algorithm which, given a set V of n points in d-dimensional space, and any constant t>1, produces a t-spanner of the complete Euclidean graph of G. The produced spanner have O(n) edges, constant degree and weight O(wt(MST)).
Funded by NSF (CCR-940-9752) and Cadence Design Systems, Inc.
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Gudmundsson, J., Levcopoulos, C., Narasimhan, G. (2000). Improved Greedy Algorithms for Constructing Sparse Geometric Spanners. In: Algorithm Theory - SWAT 2000. SWAT 2000. Lecture Notes in Computer Science, vol 1851. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44985-X_28
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DOI: https://doi.org/10.1007/3-540-44985-X_28
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