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.

• Type: Conference
• Year: 2005
• Where: COCOON
• Authors: Eyal Ackerman, Gill Barequet, Ron Y. Pinter
• Keywords: COCOON 2005, Non-intersecting Axis-parallel Segments, Rectangles, Smaller Rectangles