An Efficient Self-stabilizing Distance-2 Coloring Algorithm

We present a self-stabilizing algorithm for the distance-2 coloring problem that uses a constant number of variables on each node and that stabilizes in O(Δm) moves using at most Δ + 1 colors, where Δ is the maximum degree in the graph and m is the number of edges in the graph. The analysis holds true both for the sequential and the distributed adversarial daemon model. This should be compared with the previous best self-stabilizing algorithm for this problem which stabilizes in O(nm) moves under the sequential adversarial daemon and in O(nm) time steps for the distributed adversarial daemon and which uses O(δi) variables on each node i, where δi is the degree of node i.