October 1985 - Vol. 28 No. 10

October 1985 issue cover image

Features

Research and Advances

A probability model for overflow sufficiency in small hash tables

For hash tables in which a strict physical separation exists between primary storage and storage for overflow records, with bucket capacity at least three, a complete probability model is described. A measure of hash table efficiency is introduced, called the table sufficiency index (TSI), and defined as the probability that the overflow space is sufficient assuming that the set of hashed keys has a uniform distribution. The constructed probability model may be used to compute the TSI for hash tables with parameters chosen from a restricted domain. The TSI is advocated as a tool for making decisions about the parameters of small hash tables.
Research and Advances

The P2 algorithm for dynamic calculation of quantiles and histograms without storing observations

A heuristic algorithm is proposed for dynamic calculation of the median and other quantiles. The estimates are produced dynamically as the observations are generated. The observations are not stored; therefore, the algorithm has a very small and fixed storage requirement regardless of the number of observations. This makes it ideal for implementing in a quantile chip that can be used in industrial controllers and recorders. The algorithm is further extended to histogram plotting. The accuracy of the algorithm is analyzed.

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