Analysis of An Approximate Median Selection Algorithm Domenico Cantone Universit` a di Catania, Dipartimento di Matematica e Informatica, Viale A. Doria 6, I-95125 Catania, Italy e-mail:cantone@dmi.unict.it Micha Hofri Department of Computer Science, WPI 100 Institute Road, Worcester MA 01609-2280 e-mail:hofri@cs.wpi.edu August 10, 2006 Abstract We present analysis of an efficient algorithm for the approximate median selection problem that has been rediscovered many times, and easy to implement. The contribution of the article is in precise characterization of the accuracy of the algorithm. We present analytical results of the performance of the algorithm, as well as experimental illustrations of its precision. ∗ 1. Introduction In this paper we present an efficient algorithm for the approximate median selection problem, and its anal- ysis. The algorithm can be used on data in an array, and it works then in-place, requiring no extra space. It can be used to process a read-once stream of values, and then, by the time n items have been processed, the amount of storage it needs is in Θ(log n). The algorithm is not new, we found. In fact, it seems to have been rediscovered many times. Rousseeuw and Bassett exclaim in [12] that each of them discovered it independently, and several other expositions with the same basic idea have been published. The earliest sources for it we have found are [13] and [14]. Our contribution is in advancing its analysis beyond what has been shown so far. ∗ An early version of the work was presented in CIAC 2000 Rome, Italy, [1]