Linear-Time In-Place Selection with ε.N Element Moves

keywords: Algorithms, in-place selection, sorting
We present a new in-place selection algorithm that finds the k rm th smallest element in an array of n elements in linear time, using only ε.n element moves. Here ε>0 denotes an arbitrarily small, but fixed, real constant. As a consequence, partitioning the array in-place into segments of elements with ranks smaller than, equal to, and larger than k can be performed with (1+ε).n element moves. Minimizing the sum of comparisons and moves, we get a selection algorithm using C(n)<10.236 n comparisons and M(n)<0.644 n moves. The algorithm can be further optimized, by tuning up for the given cost ratio between a single move and a single comparison. As an example, we present an algorithm with C(n)+10.M(n)leq 13.634n.
reference: Vol. 25, 2006, No. 4, pp. 333–350