License: 
Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2021.10
URN: urn:nbn:de:0030-drops-140790
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14079/
Agarwal, Pankaj K. ;
Steiger, Alex
An Output-Sensitive Algorithm for Computing the Union of Cubes and Fat Boxes in 3D
Abstract
Let C be a set of n axis-aligned cubes of arbitrary sizes in ℝ³. Let U be their union, and let κ be the number of vertices on ∂U; κ can vary between O(1) and O(n²). We show that U can be computed in O(n log³ n + κ) time if C is in general position. The algorithm also computes the union of a set of fat boxes (i.e., boxes with bounded aspect ratio) within the same time bound. If the cubes in C are congruent or have bounded depth, the running time improves to O(n log² n), and if both conditions hold, the running time improves to O(n log n).
BibTeX - Entry
@InProceedings{agarwal_et_al:LIPIcs.ICALP.2021.10,
author = {Agarwal, Pankaj K. and Steiger, Alex},
title = {{An Output-Sensitive Algorithm for Computing the Union of Cubes and Fat Boxes in 3D}},
booktitle = {48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
pages = {10:1--10:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-195-5},
ISSN = {1868-8969},
year = {2021},
volume = {198},
editor = {Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2021/14079},
URN = {urn:nbn:de:0030-drops-140790},
doi = {10.4230/LIPIcs.ICALP.2021.10},
annote = {Keywords: union of cubes, fat boxes, plane-sweep}
}
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Keywords: |
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union of cubes, fat boxes, plane-sweep |
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Collection: |
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48th International Colloquium on Automata, Languages, and Programming (ICALP 2021) |
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Issue Date: |
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2021 |
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Date of publication: |
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02.07.2021 |
