Fast, responsive decentralized graph coloring

Graph coloring problem arises in numerous networking applications. We solve it in a fully decentralized way (ı.e., with no message passing). We propose a novel algorithm that is automatically responsive to topology changes, and we prove that it converges to a proper coloring in O(NlogN) time with high probability for generic graphs, when the number of available colors is greater than Δ , the maximum degree of the graph, and in O(logN) time if Δ=O(1) . We believe the proof techniques used in this paper are of independent interest and provide new insight into the properties required to ensure fast convergence of decentralized algorithms.