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Perfect Storage Representations for Families of Data Structures

By F. R. K. Chung and A. L. Rosenberg


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

Year: 1983
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