Linear-Time In-Place Selection with epsilon.n Element Moves

Year, pages: 2006, 333 - 350

We present a new in-place selection algorithm that finds the k-th smallest element in an array of n elements in linear time, using only epsilon.n element moves. Here epsilon>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+epsilon).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)<= 13.634n.

Kollár, J., Geffert, V. 2006. Linear-Time In-Place Selection with epsilon.n Element Moves. In Computing and Informatics, vol. 25, no.4, pp. 333-350. 1335-9150.

Kollár, J., Geffert, V. (2006). Linear-Time In-Place Selection with epsilon.n Element Moves. Computing and Informatics, 25(4), 333-350. 1335-9150.