On the union complexity of families of axis-parallel rectangles with a low packing number

Chaya Keller; Shakhar Smorodinsky

doi:10.37236/6792

On the union complexity of families of axis-parallel rectangles with a low packing number

Chaya Keller, Shakhar Smorodinsky

Ben-Gurion University of the Negev

Research output: Contribution to journal › Article › peer-review

Abstract

Let R be a family of n axis-parallel rectangles with packing number p − 1, meaning that among any p of the rectangles, there are two with a non-empty intersection. We show that the union complexity of R is at most O(n + p²), and that the (k − 1)-level complexity of R is at most O(n + kp²). Both upper bounds are tight.

Original language	English
Article number	#P4.32
Journal	Electronic Journal of Combinatorics
Volume	25
Issue number	4
DOIs	https://doi.org/10.37236/6792
State	Published - 1 Jan 2018

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics
Applied Mathematics

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Cite this

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On the union complexity of families of axis-parallel rectangles with a low packing number

Abstract

All Science Journal Classification (ASJC) codes

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