Limiting The Search for 2-Dimensional Optimal Alphabetic Trees

Two-dimensional alphabetic trees have many applications in a wide variety of diverse fields. Although, a relatively fast algorithm that finds an approximate optimal alphabetic tree (OAT) does exist, yet, the only way to find the exact one is to use dynamic programming. In dynamic programming the (OAT) is found by simply examining all nodes in the two dimensional array of weights as possible roots (cuts) at each level of the tree and finding the one with minimal cost. In this paper, we introduce the concept of for each cut to limit the search for an optimal solution. The measure of goodness is a value we call the expense of the cut, only cuts with expense less than a given limit L are considered good cuts. Then at each level of the tree, only good cuts are tested as possible candidates for an optimal solution.