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The problem of coloring the edges of an $n$-node graph of maximum degree $Delta$ with $2Delta - 1$ colors is one of the key symmetry breaking problems in the area of distributed graph algorithms. While there has been a lot of progress towards the understanding of this problem, the dependency of the running time on $Delta$ has been a long-standing open question. Very recently, Kuhn [SODA 20] showed that the problem can be solved in time $2^{O(sqrt{logDelta})}+O(log^* n)$. In this paper, we study the edge coloring problem in the distributed LOCAL model. We show that the $(mathit{degree}+1)$-list edge coloring problem, and thus also the $(2Delta-1)$-edge coloring problem, can be solved deterministically in time $log^{O(loglogDelta)}Delta + O(log^* n)$. This is a significant improvement over the result of Kuhn [SODA 20].
In this paper we study fractional coloring from the angle of distributed computing. Fractional coloring is the linear relaxation of the classical notion of coloring, and has many applications, in particular in scheduling. It was proved by Hasemann, H
We show that the $(degree+1)$-list coloring problem can be solved deterministically in $O(D cdot log n cdotlog^2Delta)$ rounds in the CONGEST model, where $D$ is the diameter of the graph, $n$ the number of nodes, and $Delta$ the maximum degree. Usin
We present a randomized distributed algorithm that computes a $Delta$-coloring in any non-complete graph with maximum degree $Delta geq 4$ in $O(log Delta) + 2^{O(sqrt{loglog n})}$ rounds, as well as a randomized algorithm that computes a $Delta$-col
We give efficient randomized and deterministic distributed algorithms for computing a distance-$2$ vertex coloring of a graph $G$ in the CONGEST model. In particular, if $Delta$ is the maximum degree of $G$, we show that there is a randomized CONGEST
We study the maximum cardinality matching problem in a standard distributed setting, where the nodes $V$ of a given $n$-node network graph $G=(V,E)$ communicate over the edges $E$ in synchronous rounds. More specifically, we consider the distributed