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

Chaya Keller, Shakhar Smorodinsky

Research output: Contribution to journalArticlepeer-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 languageEnglish
Article number#P4.32
JournalElectronic Journal of Combinatorics
Volume25
Issue number4
DOIs
StatePublished - 1 Jan 2018

ASJC Scopus subject areas

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

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