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(Δ2 m) moves using at most Δ2 + 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(n 3 m) time steps for the distributed adversarial daemon and which uses O(δ i ) variables on each node i, where δ i is the degree of node i.
KeywordsBipartite Graph Planar Graph Step Complexity Coloring Algorithm Frequency Assignment Problem
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