TY - JOUR
AU - Geffert, Viliam
AU - Kollár, Ján
PY - 2012/01/30
Y2 - 2024/08/07
TI - Linear-Time In-Place Selection with epsilon.n Element Moves
JF - COMPUTING AND INFORMATICS
JA - Comput. Inform.
VL - 25
IS - 4
SE - Articles
DO -
UR - https://www.cai.sk/ojs/index.php/cai/article/view/345
SP - 333-350
AB - 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.
ER -