An upper bound on the number of rectangulations of a point set

Abstract

We consider the number of different ways to divide a rectangle containing n noncorectilinear points into smaller rectangles by n non-intersecting axis-parallel segments, such that every point is on a segment. Using a novel counting technique of Santos and Seidel [12], we show an upper bound of O(20n/n4) on this number. © Springer-Verlag Berlin Heidelberg 2005.