The P^2 algorithm for dynamic calculation of quantiles and histograms without storing observations (pdf)

by Raj Jain, Washington University in St. Louis, and Imrich Chlamatac, Università degli Studi di Trento and other places

"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.


The advantage of the P^2 algorithm is that observations need not to be stored and no prior knowledge of the range of values is required. The storage requirement of the proposed algorithm is small and fixed, regardless of the number of observations."

Download the full article (pdf):

The new technique that has been introduced enables the calculation of quantiles and histograms in time without having to keep track of each observation. This method is highly flexible as it processes and evaluates data as it becomes available. By eliminating the need to store every data point this approach optimizes memory usage making it especially beneficial, for systems with limited storage capacity. With its efficient design this innovation has the potential to transform applications that require quantile assessments and histogram generation providing a streamlined solution, in environments where handling large amounts of data is crucial. (


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