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(N log N) 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.