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COMGEO
2006
ACM
13 years 7 months ago
Compatible triangulations and point partitions by series-triangular graphs
We introduce series-triangular graph embeddings and show how to partition point sets with them. This result is then used to prove an upper bound on the number of Steiner points nee...
Jeff Danciger, Satyan L. Devadoss, Don Sheehy
CORR
2010
Springer
168views Education» more  CORR 2010»
13 years 4 months ago
Bounds on the maximum multiplicity of some common geometric graphs
We obtain new lower and upper bounds for the maximum multiplicity of some weighted and, respectively, non-weighted common geometric graphs drawn on n points in the plane in genera...
Adrian Dumitrescu, André Schulz, Adam Sheff...
ALGORITHMICA
2005
108views more  ALGORITHMICA 2005»
13 years 7 months ago
How Fast Is the k-Means Method?
We present polynomial upper and lower bounds on the number of iterations performed by the k-means method (a.k.a. Lloyd's method) for k-means clustering. Our upper bounds are ...
Sariel Har-Peled, Bardia Sadri
GD
2005
Springer
14 years 1 months ago
Bar k-Visibility Graphs: Bounds on the Number of Edges, Chromatic Number, and Thickness
Let S be a set of horizontal line segments, or bars, in the plane. We say that G is a bar visibility graph, and S its bar visibility representation, if there exists a one-to-one co...
Alice M. Dean, William Evans, Ellen Gethner, Joshu...
JC
2008
68views more  JC 2008»
13 years 7 months ago
On the number of minima of a random polynomial
We give an upper bound in O(d(n+1)/2 ) for the number of critical points of a normal random polynomial. The number of minima (resp. maxima) is in O(d(n+1)/2 )Pn, where Pn is the (...
Jean-Pierre Dedieu, Gregorio Malajovich