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DOI: 10.4230/LIPIcs.STACS.2020.53
URN: urn:nbn:de:0030-drops-119145
URL: https://drops.dagstuhl.de/opus/volltexte/2020/11914/
Henzinger, Monika ; Peng, Pan
Constant-Time Dynamic (Δ+1)-Coloring
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Abstract
We give a fully dynamic (Las-Vegas style) algorithm with constant expected amortized time per update that maintains a proper (Δ+1)-vertex coloring of a graph with maximum degree at most Δ. This improves upon the previous O(log Δ)-time algorithm by Bhattacharya et al. (SODA 2018). Our algorithm uses an approach based on assigning random ranks to vertices and does not need to maintain a hierarchical graph decomposition. We show that our result does not only have optimal running time, but is also optimal in the sense that already deciding whether a Δ-coloring exists in a dynamically changing graph with maximum degree at most Δ takes Ω(log n) time per operation.
BibTeX - Entry
@InProceedings{henzinger_et_al:LIPIcs:2020:11914,
author = {Monika Henzinger and Pan Peng},
title = {{Constant-Time Dynamic (Δ+1)-Coloring}},
booktitle = {37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)},
pages = {53:1--53:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-140-5},
ISSN = {1868-8969},
year = {2020},
volume = {154},
editor = {Christophe Paul and Markus Bl{\"a}ser},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2020/11914},
URN = {urn:nbn:de:0030-drops-119145},
doi = {10.4230/LIPIcs.STACS.2020.53},
annote = {Keywords: Dynamic graph algorithms, Graph coloring, Random sampling}
}
| Keywords: | Dynamic graph algorithms, Graph coloring, Random sampling | |
| Seminar: | 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020) | |
| Issue date: | 2020 | |
| Date of publication: | 04.03.2020 |
