Linear-time in-place selection in less than 3n comparisons

Abstract

By developing and exploiting new in-place techniques, we show that finding the element with the median value out of n elements stored in an array can be performed in-place in (2.95+∈)n (for any ∈>0) comparisons and in linear time. This is arbitrarily close to the upper bound for the same problem without space-restrictions.

To make the algorithm competitive we also try to minimize the number of element moves performed by the algorithm since this is the other critical operation. This has resulted in a trade-off between the number of comparisons and the number of moves. By minimizing the sum of the critical operations we achieve an algorithm that uses at most 3.75n comparisons and 9n moves for finding the median in-place. This is, in principle, twice as good as earlier attempts on implicit selection for both of the operations.