# A note on self-improving sorting with hidden partitions

## TL;DR

This paper introduces an optimal self-improving sorting algorithm that adapts to hidden partitions in data, achieving expected time complexity based on the entropy of the sorted output, thus improving efficiency for certain data distributions.

## Contribution

It presents a novel algorithm for self-improving sorting with hidden partitions, achieving optimal expected time proportional to the entropy of the output ranks.

## Key findings

- Algorithm runs in expected time O(H((I)) + n)
- Achieves optimality based on entropy of output ranks
- Effective for data with hidden partition structures

## Abstract

We study self-improving sorting with hidden partitions. Our result is an optimal algorithm which runs in expected time O(H(\pi(I)) + n), where I is the given input which contains n elements to be sorted, \pi(I) is the output which are the ranks of all element in I, and H(\pi(I)) denotes the entropy of the output.