The knowledge of sparsity information plays an important role in efficient determination of sparse Jacobian matrices. In a recent work, we have proposed sparsity-exploiting substitution techniques to determine Jacobian matrices. In this paper, we take a closer look at the underlying combinatorial problem. We propose a column ordering heuristic to augment the ``usable sparsity'' in the Jacobian matrix. Furthermore, we present a new elimination technique based on merging of successive columns.
Report 223, Department of Informatics, University of Bergen, January 2002.