Distinguishing virtual braids in polynomial time

TL;DR

This paper presents a polynomial-time algorithm for determining whether a given virtual braid word is trivial, significantly advancing computational methods in virtual braid theory.

Contribution

It introduces an $O(l^3n)$-time algorithm for the triviality problem in virtual braid groups, improving efficiency over previous approaches.

Findings

Algorithm runs in polynomial time $O(l^3n)$

Efficiently solves the triviality problem for virtual braids

Advances computational group theory for virtual braids

Abstract

For $n \geq 2$ we describe an $O(l^3n)$-time algorithm that determines if a length $l$ virtual braid word in the standard presentation of the virtual braid group ${\mathcal VB}_n$ represents the trivial virtual braid.