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The Basic Greedy Graph Coloring Heuristic

Multi-coloring a graph G is an NP-complete problem that attempts to define a minimum number of colors for the nodes of a graph where no adjacent nodes are assigned the same color [27,32,42]. A greedy polynomial time heuristic can yield an optimal ordering if the nodes are visited in the correct order, although the same heuristic may be arbitrarily bad for a different order [5]. The basic greedy graph coloring heuristic is presented in figure gif. The only aspect of the basic heuristic that is normally modified, as variations on this algorithm are developed, is the rule to select the node from the remaining uncolored nodes [32]. In adding load-balancing, we have also modified the selection of the smallest available consistent color.

 
Figure: The Graph Multi-Coloring Algorithm 



David P. Koester
Sun Oct 22 17:27:14 EDT 1995