(Δ+1) Coloring in the Congested Clique Model
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In this paper, we present improved algorithms for the (Δ+1) (vertex) coloring problem in the Congested-Clique model of distributed computing. In this model, the input is a graph on n nodes, initially each node knows only its incident edges, and per round each two nodes can exchange O( n) bits of information. Our key result is a randomized (Δ+1) vertex coloring algorithm that works in O(Δ·^* Δ)-rounds. This is achieved by combining the recent breakthrough result of [Chang-Li-Pettie, STOC'18] in the model and a degree reduction technique. We also get the following results with high probability: (1) (Δ+1)-coloring for Δ=O((n/ n)^1-ϵ) for any ϵ∈ (0,1), within O((1/ϵ)^* Δ) rounds, and (2) (Δ+Δ^1/2+o(1))-coloring within O(^* Δ) rounds. Turning to deterministic algorithms, we show a (Δ+1)-coloring algorithm that works in O(Δ) rounds.
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