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

Authors:
Eyal Ackerman;Gill Barequet;Ron Y. Pinter
Affiliations:
Dept. of Computer Science, Technion–Israel Institute of Technology, Haifa, Israel;Dept. of Computer Science, Technion–Israel Institute of Technology, Haifa, Israel;Dept. of Computer Science, Technion–Israel Institute of Technology, Haifa, Israel
Venue:
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Year:
2005

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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.