Through a series of theorems they show that the factorial coding problem can be accurately solved with a branch and bound search tree algorithm, or tightly approximated with a series of linear problems. In addition, they introduce a simple transformation (namely, order permutation) which provides a greedy yet very effective approximation of the optimal solution.
By means of a series of mathematical proofs, they prove that the factorial coding problem can be efficiently solved using a branch and bound search tree algorithm or approximated closely through a set of linear problems. Additionally, they introduce a simple transformation (order permutation) that provides a heuristic yet highly effective approach to finding the optimal solution.