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

Eyal Ackerman; Gill Barequet; Ron Y. Pinter

doi:10.1007/11533719_56

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

Eyal Ackerman, Gill Barequet, Ron Y. Pinter

Research output: Contribution to journal › Conference article › peer-review

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.

Original language	English
Pages (from-to)	554-559
Number of pages	6
Journal	Lecture Notes in Computer Science
Volume	3595
DOIs	https://doi.org/10.1007/11533719_56
State	Published - 2005
Externally published	Yes
Event	11th Annual International Conference on Computing and Combinatorics, COCOON 2005 - Kunming, China Duration: 16 Aug 2005 → 29 Aug 2005

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

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10.1007/11533719_56

Cite this

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title = "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.",

author = "Eyal Ackerman and Gill Barequet and Pinter, {Ron Y.}",

year = "2005",

doi = "10.1007/11533719_56",

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AU - Ackerman, Eyal

AU - Barequet, Gill

AU - Pinter, Ron Y.

PY - 2005

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N2 - 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.

AB - 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.

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U2 - 10.1007/11533719_56

DO - 10.1007/11533719_56

M3 - Conference article

AN - SCOPUS:26844543289

SN - 0302-9743

VL - 3595

SP - 554

EP - 559

JO - Lecture Notes in Computer Science

JF - Lecture Notes in Computer Science

T2 - 11th Annual International Conference on Computing and Combinatorics, COCOON 2005

Y2 - 16 August 2005 through 29 August 2005

ER -

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

Abstract

ASJC Scopus subject areas

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