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DOI: 10.4230/LIPIcs.SoCG.2016.10
URN: urn:nbn:de:0030-drops-59024
URL: https://drops.dagstuhl.de/opus/volltexte/2016/5902/
Aronov, Boris ; Cheong, Otfried ; Dobbins, Michael Gene ; Goaoc, Xavier
The Number of Holes in the Union of Translates of a Convex Set in Three Dimensions
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Abstract
We show that the union of translates of a convex body in three dimensional space can have a cubic number holes in the worst case, where a hole in a set is a connected component of its compliment. This refutes a 20-year-old conjecture. As a consequence, we also obtain improved lower bounds on the complexity of motion planning problems and of Voronoi diagrams with convex distance functions.
BibTeX - Entry
@InProceedings{aronov_et_al:LIPIcs:2016:5902,
author = {Boris Aronov and Otfried Cheong and Michael Gene Dobbins and Xavier Goaoc},
title = {{The Number of Holes in the Union of Translates of a Convex Set in Three Dimensions}},
booktitle = {32nd International Symposium on Computational Geometry (SoCG 2016)},
pages = {10:1--10:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-009-5},
ISSN = {1868-8969},
year = {2016},
volume = {51},
editor = {S{\'a}ndor Fekete and Anna Lubiw},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2016/5902},
URN = {urn:nbn:de:0030-drops-59024},
doi = {10.4230/LIPIcs.SoCG.2016.10},
annote = {Keywords: Union complexity, Convex sets, Motion planning}
}
| Keywords: | Union complexity, Convex sets, Motion planning | |
| Seminar: | 32nd International Symposium on Computational Geometry (SoCG 2016) | |
| Issue date: | 2016 | |
| Date of publication: | 10.06.2016 |
