Abstract

Abstract. In this paper we investigate the problem of finding efficient universal storage representations for certain families of data structures, such as the family Tn of n-node binary trees, where the constituent parts of family members are labelled according to a uniform naming scheme. For example, each node of a tree in T n can be labelled by a binary string describing the sequence of left and right edges taken to reach that node from the root. If one preassigns a distinct memory location to each possible distinct name, then any member ofT n can be stored by storing the contents of each node in the location assigned to the label of that node. However, this would require 2n--1 memory locations and is wasteful of space, since certain labels can never occur together in a tree in Tn and hence could share a single memory location. We consider the problem of minimizing the number of memory locations needed, viewed in the following general form: Consider a collection I of labelled finite graphs, where each graph has distinctly labelled vertices but different graphs in I may share certain vertex labels. A graph U is universal for I ifUcontains every graph G E F as a subgraph; f is perfect-universal for I if it is universal and there exists a perfect hash function h that maps the labels of graphs in I to vertices of U such that h is one-to-one on the vertex labels of eachG E I.

Citations