2026-08-16T11:57:44Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:17217 2024-03-06T10:59:15Z ddc:004 open_access

Fast Distributed Vertex Splitting with Applications Halldórsson, Magnús M. Maus, Yannic Nolin, Alexandre Graph problems Edge coloring List coloring Lovász local lemma LOCAL model CONGEST model Distributed computing We present poly log log n-round randomized distributed algorithms to compute vertex splittings, a partition of the vertices of a graph into k parts such that a node of degree d(u) has ≈ d(u)/k neighbors in each part. Our techniques can be seen as the first progress towards general poly log log n-round algorithms for the Lovász Local Lemma. As the main application of our result, we obtain a randomized poly log log n-round CONGEST algorithm for (1+ε)Δ-edge coloring n-node graphs of sufficiently large constant maximum degree Δ, for any ε > 0. Further, our results improve the computation of defective colorings and certain tight list coloring problems. All the results improve the state-of-the-art round complexity exponentially, even in the LOCAL model. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Magnús M. Halldórsson and Yannic Maus and Alexandre Nolin 2022 Is Part Of LIPIcs, Volume 246, 36th International Symposium on Distributed Computing (DISC 2022) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.DISC.2022.26 urn:nbn:de:0030-drops-172176 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2022.26 eng https://creativecommons.org/licenses/by/4.0/legalcode