In the paper we review the most popular on-line and off-line graph coloring algorithms. For each algorithm we give: short description. performance guarantee, the smallest HC and slightly HC graphs, positive cases and negative cases. Finally, we give the smallest benchmark for off-line sequential algorithms and the smallest weak benchmark for on-line algorithms.
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An on-line algorithm that uses an adaptive learning rate is proposed. Its development is based on the analysis of the convergence of the conventional gradient descent method for three-layer BP neural networks. The effectiveness of the proposed algorithm applied to the identification and prediction of behavior of non-linear dynamic systems is demonstrated by simulation experiments.
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