Sorting and/by merging finger trees

Abstract

We describe a sorting algorithm that is optimally adaptive with respect to several important measures of presortedness. In particular, the algorithm requires O(n log(k/n)) time on sequences with k inversions; O(n-F k log k) time on sequences X that have a longest ascending subsequence of length n - k and for which Rera(X) = k; and O(nlog k) time on sequences that can be decomposed into k monotone shuffles. The algorithm makes use of an adaptive merging operation implemented using finger search trees.