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An improved approximation algorithm for the discrete Fréchet distance
TLDR
We compute an approximation to the discrete Frechet distance in time O ( n log ⁡ n + n 2 / f 2 ) for two sequences of n points in R d . Expand
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Kinetic data structures for all nearest neighbors and closest pair in the plane
TLDR
This paper presents a kinetic data structure (KDS) for solutions to the all nearest neighbors problem and the closest pair problem in the plane. Expand
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A simple, faster method for kinetic proximity problems
TLDR
This paper presents simple kinetic data structures (KDSs) for solutions to some fundamental proximity problems, namely, the all nearest neighbors problem, the closest pair problem, and the Euclidean minimum spanning tree. Expand
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Simple, Faster Kinetic Data Structures
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Kinetic Euclidean minimum spanning tree in the plane
TLDR
This paper presents a kinetic data structure (KDS) for maintenance of the Euclidean minimum spanning tree (EMST) on a set of moving points in 2-dimensional space by which the EMST is maintained efficiently during the motion. Expand
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Kinetic Pie Delaunay Graph and Its Applications
TLDR
We construct a new proximity graph, called the Pie Delaunay graph, on a set of n points which is a super graph of Yaograph and Euclidean minimum spanning tree (EMST). Expand
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Approximating the Minimum Closest Pair Distance and Nearest Neighbor Distances of Linearly Moving Points
TLDR
We present an O ź ( n 5 / 3 ) -time algorithm1 to compute a ( 1 + ź ) -factor approximation to the minimum closest pair distance over time, for any constant ź 0 and any constant dimension d. Expand
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Kinetic and Stationary Point-Set Embeddability for Plane Graphs
We investigate a kinetic version of point-set embeddability. Given a plane graph G(V,E) where |V|=n, and a set P of n moving points where the trajectory of each point is an algebraic function ofExpand
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Kinetic Data Structures for the Semi-Yao Graph and All Nearest Neighbors in $\mathbb{R}^d$
TLDR
This paper presents kinetic data structures (KDS’s) for maintaining the Semi-Yao graph, all the nearest neighbors, and all the (1 + )-nearest neighbors of a set of moving points in R. Expand
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Kinetic Data Structures for the Semi-Yao Graph and All Nearest Neighbors in R^d
TLDR
This paper presents a simple kinetic data structure for maintaining the edges of the Semi-Yao graph, a sparse graph whose edge set includes the pairs of nearest neighbors as a subset. Expand
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