Abstract

Let S be a family of n points in E a. The exact fitting problem asks for finding a hyperplane containing the maximum number of points of $. In this paper, we present an O (rain j' " " }) ,a-h-a-- log , n d time algorithm where m denoted the number of points the hyperplane. This algorithm is based on upper bounds on the maximum number of incidences between families of points and families ofhyperplanes in E d and on an algorithm to compute these incidences. We also show how the upper bound on the maximum number of incidences between families of points and families of hyperplanes can be used to derive new bounds on some well-known problems in discrete geometry.

Citations