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.SoCG.2023.54
URN: urn:nbn:de:0030-drops-179047
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/17904/
Qi, Benjamin ;
Qi, Richard
New Approximation Algorithms for Touring Regions
Abstract
We analyze the touring regions problem: find a (1+ε)-approximate Euclidean shortest path in d-dimensional space that starts at a given starting point, ends at a given ending point, and visits given regions R₁, R₂, R₃, … , R_n in that order.
Our main result is an O (n/√ε log{1/ε} + 1/ε)-time algorithm for touring disjoint disks. We also give an O(min(n/ε, n²/√ε))-time algorithm for touring disjoint two-dimensional convex fat bodies. Both of these results naturally generalize to larger dimensions; we obtain O(n/{ε^{d-1}} log²1/ε + 1/ε^{2d-2}) and O(n/ε^{2d-2})-time algorithms for touring disjoint d-dimensional balls and convex fat bodies, respectively.
BibTeX - Entry
@InProceedings{qi_et_al:LIPIcs.SoCG.2023.54,
author = {Qi, Benjamin and Qi, Richard},
title = {{New Approximation Algorithms for Touring Regions}},
booktitle = {39th International Symposium on Computational Geometry (SoCG 2023)},
pages = {54:1--54:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-273-0},
ISSN = {1868-8969},
year = {2023},
volume = {258},
editor = {Chambers, Erin W. and Gudmundsson, Joachim},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2023/17904},
URN = {urn:nbn:de:0030-drops-179047},
doi = {10.4230/LIPIcs.SoCG.2023.54},
annote = {Keywords: shortest paths, convex bodies, fat objects, disks}
}
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Keywords: |
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shortest paths, convex bodies, fat objects, disks |
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Collection: |
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39th International Symposium on Computational Geometry (SoCG 2023) |
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Issue Date: |
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2023 |
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Date of publication: |
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09.06.2023 |
