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» A bound on the number of points of a plane curve
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COMPGEOM
2009
ACM
14 years 1 months ago
k-means requires exponentially many iterations even in the plane
The k-means algorithm is a well-known method for partitioning n points that lie in the d-dimensional space into k clusters. Its main features are simplicity and speed in practice....
Andrea Vattani
FOCS
2006
IEEE
14 years 2 months ago
Points on Computable Curves
The “analyst’s traveling salesman theorem” of geometric measure theory characterizes those subsets of Euclidean space that are contained in curves of finite length. This re...
Xiaoyang Gu, Jack H. Lutz, Elvira Mayordomo
DAM
2006
124views more  DAM 2006»
13 years 8 months ago
Coloring copoints of a planar point set
To a set of n points in the plane, one can associate a graph that has less than n2 vertices and has the property that k-cliques in the graph correspond vertex sets of convex k-gon...
Walter Morris
COMGEO
2008
ACM
13 years 8 months ago
Approximation of an open polygonal curve with a minimum number of circular arcs and biarcs
We present an algorithm for approximating a given open polygonal curve with a minimum number of circular arcs. In computer-aided manufacturing environments, the paths of cutting t...
Robert L. Scot Drysdale, Günter Rote, Astrid ...
COMPGEOM
2006
ACM
14 years 2 months ago
Random triangulations of planar point sets
Let S be a finite set of n + 3 points in general position in the plane, with 3 extreme points and n interior points. We consider triangulations drawn uniformly at random from the...
Micha Sharir, Emo Welzl