An $\mathcal{O}(n)$ Space Construction of Superpermutations

TL;DR

This paper presents a novel algorithm for constructing superpermutations that significantly reduces memory usage and improves scalability, enabling the creation of larger sequences than previously possible.

Contribution

It introduces a direct, compact construction method for superpermutations, overcoming limitations of traditional recursive and graph-based approaches.

Findings

Reduces memory requirements for superpermutation construction

Enables construction of larger superpermutations

Outperforms existing methods in efficiency and scalability

Abstract

A superpermutation is a sequence that contains every permutation of $n$ distinct symbols as a contiguous substring. For instance, a valid example for three symbols is a sequence that contains all six permutations. This paper introduces a new algorithm that constructs such sequences more efficiently than existing recursive and graph-theoretic methods. Unlike traditional techniques that suffer from scalability and factorial memory demands, the proposed approach builds superpermutations directly and compactly. This improves memory usage, enabling the construction of larger sequences previously considered impractical.