The Expected Number of Extreme Discs

Expected Number of Local Maxima of Some Gaussian Random Polnomials

On the oscillation of the expected number of extreme points of a random set

Absfract: Let EN, be the expected number of extreme points among n i.i.d. points with a common radially symmetric distribution in the plane. We show that for any monotone sequence wn t co and for every e z 0, there exists a radially symmetric distribution for which EN,, 2 n/w,, infinitely often and EN, d 4+ E infinitely often. In addition, there exists a unimodal radially symmetric density such...

The expected number of extreme points of a random linear program

There has been increasing attention recently on average case algorithmic performance measures since worst case measures can be qualitatively quite different. An important characteristic of a linear program, relating to Simplex Method performance, is the number of vertices of the feasible region. We show 2 ~ to be an upper bound on the mean number of extreme points of a randomly generated feasib...

expected number of local maxima of some gaussian random polnomials

The Expected Number of k-faces of a Voronoi Diagram

d01 n and 8 d01 n edges in the Voronoi dual. The lower bound of Theorem 1 for k = 1 is equal to the expected number of edges of the Gabriel graph, and agrees with Devroye's results [2]. When k > 1, the Gabriel ball can extend arbitrarily far from the sites that dene it, and this apparently makes it impossible to extend our results to the broad classes of distributions Devroye treated for k = 1....