Graph coloring in the estimation of sparse derivative matrices: Instances and applications

We describe a graph coloring problem associated with the determination of mathematical derivatives. The coloring instances are obtained as intersection graphs of row partitioned sparse derivative matrices. The size of the graph is dependent on the partition and can be varied between the number of columns and the number of nonzero entries. If solved exactly our proposal will yield a significant reduction in computational cost of the derivative matrices. The effectiveness of our approach is demonstrated via a practical problem from computational molecular biology. We also remark on the hardness of the generated coloring instances.