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...
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...
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 ...
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...
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 (...