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625
The emergence of sparse spanners and greedy wellseparated pair decomposition
, 2009
"... A spanner graph on a set of points in Rd contains a shortest path between any pair of points with length at most a constant factor of their Euclidean distance. A spanner with a sparse set of edges is thus a good candidate for network backbones, as desired in many practical scenarios such as the tran ..."
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Cited by 2 (2 self)
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a sparse spanner as desired. This new spanner construction algorithm can be extended to a metric space with constant doubling dimension and admits a local routing scheme to find the short paths. As a side product, we show a greedy algorithm for constructing linearsize wellseparated pair
THE EMERGENCE OF SPARSE SPANNERS AND WELLSEPARATED PAIR DECOMPOSITION UNDER ANARCHY
 JOURNAL OF COMPUTATIONAL GEOMETRY
, 2012
"... A spanner graph on a set of points in Rd provides shortest paths between any pair of points with lengths at most a constant factor of their Euclidean distance. A spanner with a sparse set of edges is thus a good candidate for network backbones, as desired in many practical scenarios such as the tra ..."
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of constructing an edge pq, if and only if there is no existing edge p ′ q ′ with p ′ and q ′ at 1 distances no more than 4(1+1/ε) · pq  from p, q respectively, generates a (1 + ε)spanner with a linear number of edges. The algorithm also implies a simple algorithm for constructing linearsize wellseparated
Pruning spanners and constructing wellseparated pair decompositions in the presence of memory hierarchies
, 2010
"... ..."
ABSTRACT WellSeparated Pair Decomposition for
"... We extend the classic notion of wellseparated pair decomposition [10] to the (weighted) unitdisk graph metric: the shortest path distance metric induced by the intersection graph of unit disks. We show that for the unitdisk graph metric of n points in the plane and for any constant c ≥ 1, there e ..."
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We extend the classic notion of wellseparated pair decomposition [10] to the (weighted) unitdisk graph metric: the shortest path distance metric induced by the intersection graph of unit disks. We show that for the unitdisk graph metric of n points in the plane and for any constant c ≥ 1
DistributionSensitive Construction of the Greedy Spanner
"... The greedy spanner is the highest quality geometric spanner (in e.g. edge count and weight, both in theory and practice) known to be computable in polynomial time. Unfortunately, all known algorithms for computing it take Ω(n2) time, limiting its applicability on large data sets. We observe that for ..."
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that for many point sets, the greedy spanner has many ‘short ’ edges that can be determined locally and usually quickly, and few or no ‘long ’ edges that can usually be determined quickly using local information and the wellseparated pair decomposition. We give experimental results showing large to massive
Wellseparated pair decomposition for the unitdisk graph metric and its applications
 SIAM Journal on Computing
, 2003
"... Abstract. We extend the classic notion of wellseparated pair decomposition [10] to the unitdisk graph metric: the shortest path distance metric induced by the intersection graph of unit disks. We show that for the unitdisk graph metric of n points in the plane and for any constant c ≥ 1, there ex ..."
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Cited by 10 (1 self)
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Abstract. We extend the classic notion of wellseparated pair decomposition [10] to the unitdisk graph metric: the shortest path distance metric induced by the intersection graph of unit disks. We show that for the unitdisk graph metric of n points in the plane and for any constant c ≥ 1
Spanning Trees and Spanners
, 1996
"... We survey results in geometric network design theory, including algorithms for constructing minimum spanning trees and lowdilation graphs. ..."
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Cited by 149 (2 self)
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We survey results in geometric network design theory, including algorithms for constructing minimum spanning trees and lowdilation graphs.
Deformable spanners and applications
 In Proc. of the 20th ACM Symposium on Computational Geometry (SoCG’04
, 2004
"... For a set S of points in R d,ansspanner is a graph on S such that any pair of points is connected via some path in the spanner whose total length is at most s times the Euclidean distance between the points. In this paper we propose a new sparse (1 + ε)spanner with O(n/ε d) edges, where ε is a spe ..."
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Cited by 52 (6 self)
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deformable spanner succinctly encodes all proximity information in a deforming point cloud, giving us efficient kinetic algorithms for problems such as the closest pair, the near neighbors of all points, approximate nearest neighbor search (aka approximate Voronoi diagram), wellseparated pair decomposition
Computing the greedy spanner in nearquadratic time
, 2008
"... The greedy algorithm produces highquality spanners and, therefore, is used in several applications. However, even for points in ddimensional Euclidean space, the greedy algorithm has nearcubic running time. In this paper, we present an algorithm that computes the greedy spanner for a set of n poi ..."
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Cited by 9 (6 self)
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The greedy algorithm produces highquality spanners and, therefore, is used in several applications. However, even for points in ddimensional Euclidean space, the greedy algorithm has nearcubic running time. In this paper, we present an algorithm that computes the greedy spanner for a set of n
Computing the greedy spanner in linear space
 In Proc. 21th European Symposium on Algorithms (ESA
, 2013
"... Abstract. The greedy spanner is a highquality spanner: its total weight, edge count and maximal degree are asymptotically optimal and in practice significantly better than for any other spanner with reasonable construction time. Unfortunately, all known algorithms that compute the greedy spanner ..."
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Cited by 1 (1 self)
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Abstract. The greedy spanner is a highquality spanner: its total weight, edge count and maximal degree are asymptotically optimal and in practice significantly better than for any other spanner with reasonable construction time. Unfortunately, all known algorithms that compute the greedy spanner
Results 1  10
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625