New Results of Fault Tolerant Geometric Spanners
WADS '99 Proceedings of the 6th International Workshop on Algorithms and Data Structures
I/O-Efficient Well-Separated Pair Decomposition and Its Applications
ESA '00 Proceedings of the 8th Annual European Symposium on Algorithms
Geometric Spanner of Objects under L1 Distance
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
On the Power of the Semi-Separated Pair Decomposition
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Deformable spanners and applications
Computational Geometry: Theory and Applications
Experimental study of geometric t-spanners: a running time comparison
WEA'07 Proceedings of the 6th international conference on Experimental algorithms
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Journal of Discrete Algorithms
I/O-Efficiently pruning dense spanners
JCDCG'04 Proceedings of the 2004 Japanese conference on Discrete and Computational Geometry
An optimal-time construction of sparse Euclidean spanners with tiny diameter
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Fast pruning of geometric spanners
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
The emergence of sparse spanners and greedy well-separated pair decomposition
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Proceedings of the twenty-ninth annual symposium on Computational geometry
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
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Let S be a set of n points in IR/sup d/ and let t1 be a real number. A t-spanner for S is a directed graph having the points of S as its vertices, such that for any pair p and q of points there is a path from p to q of length at most t times the Euclidean distance between p and p. Such a path is called a t-spanner path. The spanner diameter of such a spanner is defined as the smallest integer D such that for any pair p and q of points there is a t-spanner path from p to q containing at most D edges. Randomized and deterministic algorithms are given for constructing t-spanners consisting of O(n) edges and having O(log n) diameter. Also, it is shown how to maintain the randomized t-spanner under random insertions and deletions. Previously, no results were known for spanners with low spanner diameter and for maintaining spanners under insertions and deletions.