Ultrafast Distributed Coloring of High Degree Graphs
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We give a new randomized distributed algorithm for the Δ+1-list coloring problem. The algorithm and its analysis dramatically simplify the previous best result known of Chang, Li, and Pettie [SICOMP 2020]. This allows for numerous refinements, and in particular, we can color all n-node graphs of maximum degree Δ≥log^2+Ω(1) n in O(log^* n) rounds. The algorithm works in the CONGEST model, i.e., it uses only O(log n) bits per message for communication. On low-degree graphs, the algorithm shatters the graph into components of size poly(log n) in O(log^* Δ) rounds, showing that the randomized complexity of Δ+1-list coloring in CONGEST depends inherently on the deterministic complexity of related coloring problems.
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