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/n 4) on this number.
Work on this paper by the first author has been supported in part by a Neeman fellowship at the Technion. Work by the first and second authors has also been supported in part by the European FP6 Network of Excellence Grant 506766 (AIM@SHAPE).
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Ackerman, E., Barequet, G., Pinter, R.Y. (2005). An Upper Bound on the Number of Rectangulations of a Point Set. In: Wang, L. (eds) Computing and Combinatorics. COCOON 2005. Lecture Notes in Computer Science, vol 3595. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11533719_56
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DOI: https://doi.org/10.1007/11533719_56
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28061-3
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