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- W4366562931 abstract "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 $x_{v,1},dots,x_{v,p}$ together with a list of defects $d_{v,1},dots,d_{v,p}$ 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 $(Delta+1)$-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 $sum_{i=1}^p big(d_{v,i}+1)^2 > mathrm{deg}_G^2(v)cdot polylogDelta$ then this list defective coloring instance can be solved in a communication-efficient way in only $O(logDelta)$ communication rounds. This leads to the first deterministic $(Delta+1)$-coloring algorithm in the standard CONGEST model with a time complexity of $O(sqrt{Delta}cdot polylog Delta+log^* n)$, matching the best time complexity in the LOCAL model up to a $polylogDelta$ factor." @default.
- W4366562931 created "2023-04-22" @default.
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- W4366562931 date "2023-04-19" @default.
- W4366562931 modified "2023-10-18" @default.
- W4366562931 title "List Defective Colorings: Distributed Algorithms and Applications" @default.
- W4366562931 doi "https://doi.org/10.4230/lipics.disc.2023.22" @default.
- W4366562931 hasPublicationYear "2023" @default.
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