We consider the problem of coloring graphs of maximum degree Δ with Δ colors in the distributed setting with limited bandwidth. Specifically, we give a polylog log n-round randomized algorithm in the CONGEST model. This is close to the lower bound of Ω(log log n) rounds from [Brandt et al., STOC '16], which holds also in the more powerful LOCAL model. The core of our algorithm is a reduction to several special instances of the constructive Lovász local lemma (LLL) and the deg+1-list coloring problem.
@InProceedings{halldorsson_et_al:LIPIcs.DISC.2024.31, author = {Halld\'{o}rsson, Magn\'{u}s M. and Maus, Yannic}, title = {{Distributed Delta-Coloring Under Bandwidth Limitations}}, booktitle = {38th International Symposium on Distributed Computing (DISC 2024)}, pages = {31:1--31:22}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-352-2}, ISSN = {1868-8969}, year = {2024}, volume = {319}, editor = {Alistarh, Dan}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2024.31}, URN = {urn:nbn:de:0030-drops-212572}, doi = {10.4230/LIPIcs.DISC.2024.31}, annote = {Keywords: Graph problems, Graph coloring, Lov\'{a}sz local lemma, LOCAL model, CONGEST model, Distributed computing} }
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