2026-07-23T08:48:57Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:19148 2024-03-06T11:03:32Z ddc:004 open_access

List Defective Colorings: Distributed Algorithms and Applications Fuchs, Marc Kuhn, Fabian distributed coloring list coloring defective coloring The distributed coloring problem is at the core of the area of distributed graph algorithms and it is a problem that has seen tremendous progress over the last few years. Much of the remarkable recent progress on deterministic distributed coloring algorithms is based on two main tools: a) defective colorings in which every node of a given color can have a limited number of neighbors of the same color and b) list coloring, a natural generalization of the standard coloring problem that naturally appears when colorings are computed in different stages and one has to extend a previously computed partial coloring to a full coloring. In this paper, we introduce list defective colorings, which can be seen as a generalization of these two coloring variants. Essentially, in a list defective coloring instance, each node v is given a list of colors x_{v,1},… ,x_{v,p} together with a list of defects d_{v,1},… ,d_{v,p} such that if v is colored with color x_{v, i}, it is allowed to have at most d_{v, i} neighbors with color x_{v, i}. We highlight the important role of list defective colorings by showing that faster list defective coloring algorithms would directly lead to faster deterministic (Δ+1)-coloring algorithms in the LOCAL model. Further, we extend a recent distributed list coloring algorithm by Maus and Tonoyan [DISC '20]. Slightly simplified, we show that if for each node v it holds that ∑_{i=1}^p (d_{v,i}+1)² > deg_G²(v)⋅ polylogΔ then this list defective coloring instance can be solved in a communication-efficient way in only O(logΔ) communication rounds. This leads to the first deterministic (Δ+1)-coloring algorithm in the standard CONGEST model with a time complexity of O(√{Δ}⋅ polylog Δ+log^* n), matching the best time complexity in the LOCAL model up to a polylogΔ factor. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Marc Fuchs and Fabian Kuhn 2023 Is Part Of LIPIcs, Volume 281, 37th International Symposium on Distributed Computing (DISC 2023) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.DISC.2023.22 urn:nbn:de:0030-drops-191484 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2023.22 eng https://creativecommons.org/licenses/by/4.0/legalcode