Counting Inversions Adaptively

TL;DR

This paper presents an efficient adaptive algorithm for counting inversions in a sequence, with runtime depending on the number of inversions, improving efficiency for sequences with fewer inversions.

Contribution

The paper introduces a simple, adaptive algorithm that counts inversions in O(n + n√(log(Inv/n))) time, optimizing performance based on the sequence's disorder.

Findings

Runs in sublinear time for sequences with few inversions

Efficient in the word-RAM computational model

Improves upon previous inversion counting algorithms

Abstract

We give a simple and efficient algorithm for adaptively counting inversions in a sequence of $n$ integers. Our algorithm runs in $O(n + n \sqrt{\lg{(Inv/n)}})$ time in the word-RAM model of computation, where $Inv$ is the number of inversions.