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arXiv · 1702.00849

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

Chaya Keller·Shakhar Smorodinsky
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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+p^2), and that the (<=k)-level complexity of R is at most O(kn+k^2p^2). Both upper bounds are tight.

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Chaya Keller, Shakhar Smorodinsky. 2017-02-02. On the union complexity of families of axis-parallel rectangles with a low packing number. https://arxiv.org/abs/1702.00849

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