Compressed Representations of Permutations, and Applications

TL;DR

This paper investigates methods to efficiently compress permutations by exploiting ordered subsequences, enabling fast application of permutations and their inverses, with improvements in related data structures and applications.

Contribution

It introduces novel compression schemes for permutations that support quick application and inversion, enhancing existing methods for permutation encoding and related data structures.

Findings

Achieves improved compression ratios for permutations.

Supports fast permutation and inverse application in small time.

Extends to applications like iterated permutation and suffix arrays.

Abstract

We explore various techniques to compress a permutation $\pi$ over n integers, taking advantage of ordered subsequences in $\pi$, while supporting its application $\pi$(i) and the application of its inverse $\pi^{-1}(i)$ in small time. Our compression schemes yield several interesting byproducts, in many cases matching, improving or extending the best existing results on applications such as the encoding of a permutation in order to support iterated applications $\pi^k(i)$ of it, of integer functions, and of inverted lists and suffix arrays.