CONCURRENCY AND COMPUTATION: PRACTICE AND EXPERIENCE Concurrency Computat.: Pract. Exper. 2009; 21:2336–2354 Published online 20 July 2009 inWiley InterScience (www.interscience.wiley.com). DOI: 10.1002/cpe.1453 Deterministic parallel selection algorithms on coarse-grained multicomputers M. Cafaro 1,2,3, ∗, † , Vincenzo De Bene 4 and G. Aloisio 1,2,3 1 University of Salento, Lecce, Italy 2 National Nanotechnology Laboratory/CNR-INFM, Lecce, Italy 3 CMCC—Euro-Mediterranean Centre for Climate Change, Lecce, Italy 4 University of Salento, Lecce, Italy SUMMARY We present two deterministic parallel Selection algorithms for distributed memory machines, under the coarse-grained multicomputer model. Both are based on the use of two weighted 3-medians, that allows discarding at least 1/3 of the elements in each iteration. The first algorithm slightly improves the current experimentally fastest algorithm by Saukas and Song where at least 1/4 of the elements are discarded in each iteration, while the second one is a fast, special purpose algorithm working for a particular class of input, namely an input that can be sorted in linear time using RadixSort. Copyright © 2009 John Wiley & Sons, Ltd. Received 1 December 2008; Revised 25 February 2009; Accepted 29 March 2009 KEY WORDS: selection; weighted 3-median; RadixSort 1. INTRODUCTION Given a set A of n (distinct) elements, the rank of an element x ∈ A, denoted as rank(x , A), is the number of elements of A less than or equal to x . The problem of selecting the i th order statistics of a set of n elements [1] requires finding the i th smallest element; it can be stated formally as follows. Definition 1.1. Input: A set A of n (distinct) numbers and a number i , with 1≤i ≤n. Output: The element x ∈ A such that rank(x , A)=i . ∗ Correspondence to: M. Cafaro, Facolt` a di Ingegneria, Universit` a del Salento, Via per Monteroni, 73100 Lecce, Italy. † E-mail: massimo.cafaro@unisalento.it, massimo.cafaro@unile.it Copyright 2009 John Wiley & Sons, Ltd.