Proceedings of the international symposium on Optimal algorithms
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
On sparse spanners of weighted graphs
Discrete & Computational Geometry
Optimally sparse spanners in 3-dimensional Euclidean space
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Constructing Degree-3 Spanners with Other Sparseness Properties
ISAAC '93 Proceedings of the 4th International Symposium on Algorithms and Computation
Graph spanners
Euclidean spanners: short, thin, and lanky
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
A new way to weigh Malnourished Euclidean graphs
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Constructing the Spanners of Graphs in Parallel
IPPS '96 Proceedings of the 10th International Parallel Processing Symposium
Geometric Spanner of Objects under L1 Distance
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Computing Lightweight Spanners Locally
DISC '08 Proceedings of the 22nd international symposium on Distributed Computing
On Spanners of Geometric Graphs
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Balancing degree, diameter and weight in Euclidean spanners
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
On Spanners and Lightweight Spanners of Geometric Graphs
SIAM Journal on Computing
An optimal-time construction of sparse Euclidean spanners with tiny diameter
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Sparse fault-tolerant spanners for doubling metrics with bounded hop-diameter or degree
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Sparse Euclidean Spanners with Tiny Diameter
ACM Transactions on Algorithms (TALG) - Special Issue on SODA'11
Optimal euclidean spanners: really short, thin and lanky
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
On certain geometric properties of the Yao---Yao graphs
Journal of Combinatorial Optimization
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Let G=(V,E) be a n-vertex connected graph with positive edge weights. A subgraph G′ is a t-spanner if for all u,v ∈ V, the distance between u and v in the subgraph is at most t times the corresponding distance in G. We design an O(nlog2n) time algorithm which, given a set V of n points in k-dimensional space, and any constant t1, produces a t-spanner of the complete Euclidean graph of V. This algorithm retains the spirit of a recent O(n3logn)-time greedy algorithm which produces t-spanners with a small number of edges and a small total edge weight; we use graph clustering techniques to achieve a more efficient implementation. Our spanners have similar size and weight sparseness as those constructed by the greedy algorithm.