A generalization of AVL trees is proposed in which imbalances up to Δ are permitted, where Δ is a small integer. An experiment is performed to compare these trees with standard AVL trees and with balanced trees on the basis of mean retrieval time, of amount of restructuring expected, and on the worst case of retrieval time. It is shown that, by permitting imbalances of up to five units, the retrieval time is increased a small amount while the amount of restructuring required is decreased by a factor of ten.
A few theoretical results are derived, including the correction of an earlier paper, and are duly compared with the experimental data. Reasonably good correspondence is found.
We propose a method for implementing “the election process” - finding an extrema of values computed in a multiprocessor network. It operates in an average time less than Log2(N), for a network of size N. It requires a single register, memory cell, or global buss into which all the processors can attempt to write, with the success of one guaranteed; and from which they may all read, in parallel. A second method is given which guarantees termination in O(Log2(MAX)) steps.
A sociogram is a net in which individuals are nodes and the relations of interest are directed line segments connecting pairs of individuals. In the simplest case such a relation is characterized only by its presence or absence, e.g., “A chooses (or does not choose) B as a friend of a given rank order.” Mathematical praperties of such nets are of interest to the mathematical sociologist. If the number of individuals is very large, the properties of interest are statistical properties. Here it is shown that two parameters (whose values are obtainable directly from the data) are sufficient to describe certain features of sociograms of junior high schoal children.
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