Compactly Representable Skewing Schemes for Trees

Abstract

As pointed out in chapter 3, arbitrary skewing schemes are not always of much practical interest. In this chapter we only study compactly representable skewing schemes for trees, i.e., skewing schemes for trees which allow for a short representation and which are quickly computable. The compactly representable skewing schemes for d-dimensional arrays were obtained by requiring that whenever two elements x and y of a d-dimensional array are mapped into the same memory bank then every two points which are in the same relative position to each other as x and y are mapped into the same memory bank also. This appeared to be a natural way of defining compactly representable skewing schemes. So, we will apply the same idea to skewing schemes for trees. By this approach we obtain various kinds of compactly representable skewing schemes for trees: regular, semi-regular, linear and simple skewing schemes. As in chapter 4 we will assume that trees are infinite, complete, k-ary, and have a fixed orientation.