REPORTS IN INFORMATICS ISSN 0333-3590 Graph Coloring in Optimization Revisited

We revisit the role of graph coloring in modeling problems that arise in efficient estimation of large sparse Jacobian and Hessian matrices using both finite difference (FD) and automatic differentiation (AD) techniques, in each case via direct methods. For Jacobian estimation using column partitioning, we propose a new coloring formulation based on a bipartite graph representation. This is compared with the known column intersection graph based formulation. Moreover, we analyze existing graph coloring formulations for efficient estimation of Hessians using FD and Jacobians using AD. We identify distance-2 coloring as a unifying general problem across the different cases. We also present and analyze greedy graph coloring heuristics corresponding to each case.