The word problem for the mapping class group in quasi-linear time

TL;DR

This paper presents an efficient algorithm that solves the word problem for the mapping class group of a compact surface in quasi-linear time, significantly improving computational performance.

Contribution

It introduces an $O(n ext{log}^3(n))$-time algorithm for the word problem in the mapping class group, advancing computational methods in geometric group theory.

Findings

Algorithm runs in quasi-linear time

Solves the word problem efficiently for compact surfaces

Improves previous computational complexity bounds

Abstract

We give an $O(n \log^3(n))$-time algorithm for the word problem in the mapping class group of a compact surface.