The cyclic coloring problem and estimation of spare hessian matrices
SIAM Journal on Algebraic and Discrete Methods
The Efficient Computation of Sparse Jacobian Matrices Using Automatic Differentiation
SIAM Journal on Scientific Computing
Evaluating derivatives: principles and techniques of algorithmic differentiation
Evaluating derivatives: principles and techniques of algorithmic differentiation
New methods to color the vertices of a graph
Communications of the ACM
Frozen development in graph coloring
Theoretical Computer Science - Phase transitions in combinatorial problems
Reducing the number of AD passes for computing a sparse Jacobian matrix
Automatic differentiation of algorithms
Another look at graph coloring via propositional satisfiability
Discrete Applied Mathematics
Graph models and their efficient implementation for sparse Jacobian matrix determination
Discrete Applied Mathematics
| Hi-index | 0.04 |
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.