Computational geometry: an introduction
Computational geometry: an introduction
A sparse graph almost as good as the complete graph on points in K dimensions
Discrete & Computational Geometry
Construction of multidimensional spanner graphs, with applications to minimum spanning trees
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Classes of graphs which approximate the complete Euclidean graph
Discrete & Computational Geometry
Euclidean spanners: short, thin, and lanky
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Undirected single-source shortest paths with positive integer weights in linear time
Journal of the ACM (JACM)
Lower Bounds for Computing Geometric Spanners and Approximate Shortest Paths
Proceedings of the 8th Canadian Conference on Computational Geometry
Fast Approximation Schemes for Euclidean Multi-connectivity Problems
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Polynomial-Time Approximation Schemes for the Euclidean Survivable Network Design Problem
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
t-Spanners as a Data Structure for Metric Space Searching
SPIRE 2002 Proceedings of the 9th International Symposium on String Processing and Information Retrieval
Constructing Plane Spanners of Bounded Degree and Low Weight
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Geodesic Spanners on Polyhedral Surfaces
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
On euclidean vehicle routing with allocation
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
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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(n log n)-time algorithm which, given a set V of n points in d-dimensional space, and any constant t1, 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)).