Distance-2 Coloring in the CONGEST Model
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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 Δ is the maximum degree of G, we show that there is a randomized CONGEST model algorithm to compute a distance-2 coloring of G with Δ^2+1 colors in O(logΔ·log n) rounds. Further if the number of colors is slightly increased to (1+ϵ)Δ^2 for some ϵ>1/ polylog(n), we show that it is even possible to compute a distance-2 coloring deterministically in polylog(n) time in the CONGEST model. Finally, we give a O(Δ^2 + log^* n)-round deterministic CONGEST algorithm to compute distance-2 coloring with Δ^2+1 colors.
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