Delaunay graphs are almost as good as complete graphs
Discrete & Computational Geometry
New sparseness results on graph spanners
SCG '92 Proceedings of the eighth 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
The Delauney Triangulation Closely Approximates the Complete Euclidean Graph
WADS '89 Proceedings of the Workshop on Algorithms and Data Structures
On the Spanning Ratio of Gabriel Graphs and beta-skeletons
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
Which Triangulations Approximate the Complete Graph?
Proceedings of the International Symposium on Optimal Algorithms
Constructing Plane Spanners of Bounded Degree and Low Weight
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Localized construction of bounded degree and planar spanner for wireless ad hoc networks
DIALM-POMC '03 Proceedings of the 2003 joint workshop on Foundations of mobile computing
Localized construction of bounded degree and planar spanner for wireless ad hoc networks
DIALM-POMC '03 Proceedings of the 2003 joint workshop on Foundations of mobile computing
Applications of k-Local MST for Topology Control and Broadcasting in Wireless Ad Hoc Networks
IEEE Transactions on Parallel and Distributed Systems
Local Construction and Coloring of Spanners of Location Aware Unit Disk Graphs
Graph-Theoretic Concepts in Computer Science
Approximate MST for UDG locally
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
Half-space proximal: a new local test for extracting a bounded dilation spanner of a unit disk graph
OPODIS'05 Proceedings of the 9th international conference on Principles of Distributed Systems
Topology control with limited geometric information
OPODIS'05 Proceedings of the 9th international conference on Principles of Distributed Systems
Local construction of planar spanners in unit disk graphs with irregular transmission ranges
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
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Given a set V of n points in a two-dimensional plane, we give an O(n log n)-time centralized algorithm that constructs a planar t-spanner for V, for t le; max{π/2, π sin α/2 + 1} ċ Cdel, such that the degree of each node is bounded from above by 19 + ⌈2π/α⌉, and the total edge length is proportional to the weight of the minimum spanning tree of V, where 0 Cdel is the spanning ratio of the Delaunay triangulation, which is at most 4√3/9 π. Moreover, we show that our method can be extended to construct a planar bounded degree spanner for unit disk graphs with the adjustable parameter α satisfying 0 O(n) (under broadcasting communication model). These constants are all worst case constants due to our proofs. Previously, only centralized method [1] of constructing bounded degree planar spanner is known, with degree bound 27 and spanning ratio t ≃ 10.02. The distributed implementation of this centralized method takes O(n2) communications in the worst case.