
O(k)robust spanners in one dimension
A geometric tspanner on a set of points in Euclidean space is a graph c...
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The wellseparated pair decomposition for balls
Given a real number t>1, a geometric tspanner is a geometric graph for ...
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Nearestneighbour Markov point processes on graphs with Euclidean edges
We define nearestneighbour point processes on graphs with Euclidean edg...
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Binarized JohnsonLindenstrauss embeddings
We consider the problem of encoding a set of vectors into a minimal numb...
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FaultTolerant Additive Weighted Geometric Spanners
Let S be a set of n points and let w be a function that assigns nonnega...
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Truly Optimal Euclidean Spanners
Euclidean spanners are important geometric structures, having found nume...
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A Distance Function for Comparing StraightEdge Geometric Figures
This paper defines a distance function that measures the dissimilarity b...
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NearOptimal O(k)Robust Geometric Spanners
For any constants d> 1, ϵ >0, t>1, and any npoint set P⊂R^d, we show that there is a geometric graph G=(P,E) having O(n^4 n n) edges with the following property: For any F⊆ P, there exists F^+⊇ F, F^+ < (1+ϵ)F such that, for any pair p,q∈ P∖ F^+, the graph GF contains a path from p to q whose (Euclidean) length is at most t times the Euclidean distance between p and q. In the terminology of robust spanners (Bose 2013) the graph G is a (1+ϵ)krobust tspanner of P. This construction is more sparse than the most recent work (Buchin, Olàh, and HarPeled 2018) which proves the existence of (1+ϵ)krobust tspanners with n^O(d) n edges.
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