Fast computation of the median by successive binning

TL;DR

This paper introduces new median algorithms with linear average and worst-case running times, significantly improving update speed when data is added, and outperforming standard methods in various scenarios.

Contribution

It presents a novel median algorithm with O(n) average time and an approximation method with O(n) worst-case time, enhancing efficiency in data updates.

Findings

Algorithms are highly competitive with standard methods for single data sets.

Significantly faster median updates when adding more data.

Effective in both exact and approximate median computations.

Abstract

This paper describes a new median algorithm and a median approximation algorithm. The former has O(n) average running time and the latter has O(n) worst-case running time. These algorithms are highly competitive with the standard algorithm when computing the median of a single data set, but are significantly faster in updating the median when more data is added.