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» Computational geometry: a retrospective
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COMPGEOM
2010
ACM
15 years 11 months ago
Incidences in three dimensions and distinct distances in the plane
d Abstract] György Elekes Eötvös University Micha Sharir Tel Aviv University and New York University We first describe a reduction from the problem of lower-bounding the numbe...
György Elekes, Micha Sharir
COMPGEOM
2010
ACM
15 years 11 months ago
A kinetic triangulation scheme for moving points in the plane
We present a simple randomized scheme for triangulating a set P of n points in the plane, and construct a kinetic data structure which maintains the triangulation as the points of...
Haim Kaplan, Natan Rubin, Micha Sharir
COMPGEOM
2000
ACM
15 years 10 months ago
A trace bound for the hereditary discrepancy
Let A be the incidence matrix of a set system with m sets and n points, m ≤ n, and let t = tr M, where M = AT A. Finally, let σ = tr M2 be the sum of squares of the elements of ...
Bernard Chazelle, Alexey Lvov
COMPGEOM
2007
ACM
15 years 10 months ago
Kinetic KD-trees and longest-side KD-trees
We propose a simple variant of kd-trees, called rank-based kd-trees, for sets of points in Rd . We show that a rank-based kd-tree, like an ordinary kd-tree, supports range search ...
Mohammad Ali Abam, Mark de Berg, Bettina Speckmann
COMPGEOM
2005
ACM
15 years 8 months ago
Kinetic sorting and kinetic convex hulls
Let S be a set of n points moving on the real line. The kinetic sorting problem is to maintain a data structure on the set S that makes it possible to quickly generate a sorted li...
Mohammad Ali Abam, Mark de Berg