Linear time self-stabilizing colorings

We propose two new self-stabilizing distributed algorithms for proper ∆+1 (∆ is the maximum degree of a node in the graph) colorings of arbitrary system graphs. Both algorithms are capable of working with multiple type of daemons (schedulers) as is the most recent algorithm by Gradinariu and Tixeuil [OPODIS’2000, 2000, pp. 55–70]. The first algorithm converges in O(m) moves while the second converges in at most n moves (n is the number of nodes and m is the number of edges in the graph) as opposed to the O(∆ × n) moves required by the algorithm by Gradinariu and Tixeuil [OPODIS’2000, 2000, pp. 55–70]. The second improvement is that neither of the proposed algorithms requires each node to have knowledge of ∆, as is required by Gradinariu and Tixeuil [OPODIS’2000, 2000, pp. 55–70]. Further, the coloring produced by our first algorithm provides an interesting type of coloring, called a Grundy Coloring [Jensen and Toft, Graph Coloring Problems, 1995].  2003 Elsevier B.V. All rights reserved.