Abstract:
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 Δ2 + 1 colors in O(log Δ · log n) rounds. Further if the number of colors is slightly increased to (1 + ∈)Δ2 for some ∈ > 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(Δ2 + log* n)-round deterministic CONGEST algorithm to compute distance-2 coloring with Δ2 + 1 colors.
