Iterated greedy graph coloring and the coloring landscape
The Iterated Greedy (IG) graph coloring algorithm uses the greedy, or simple sequential, graph coloring algorithm repeatedly to obtain ever better colorings. On each iteration, the permutation presented to the greedy algorithm is generated so that the vertices of the independent sets identified in the previous coloring are adjacent in the permutation. It is trivial to prove that this ensures that the new coloring will use no more colors than the previous coloring. On random graphs the algorithm does not perform as well as TABU or semi-exhaustive independent set approaches. It does offer some improvements when combined with these. On k-colorable graphs it seems quite effective, and offers a robustness over a wide range of k, n, p values the other algorithms seem not to have. In particular, evidence indicates that one setting of parameters seems to be {open_quotes}near best{close_quotes} over most of these classes. Evidence also indicates that graphs in the classes we consider that are harder for this algorithm are also more difficult for TABU and semi-exhaustive independent set approaches. Thus, the number of iterations required gives a natural measure of difficulty of the graphs, independent of machine characteristics and many details of implementation.
- OSTI ID:
- 35928
- Report Number(s):
- CONF-9408161--
- Country of Publication:
- United States
- Language:
- English
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