Compressed conjugacy and the word problem for outer automorphism groups of graph groups

TL;DR

This paper demonstrates that the conjugacy and word problems for outer automorphism groups of graph groups can be efficiently solved in polynomial time, even with compressed input representations, advancing computational group theory.

Contribution

It introduces polynomial-time algorithms for conjugacy and word problems in outer automorphism groups of graph groups with compressed inputs.

Findings

Conjugacy problem solvable in polynomial time for graph groups

Word problem for outer automorphism groups solvable in polynomial time

Efficient algorithms for compressed input representations

Abstract

It is shown that for graph groups (right-angled Artin groups) the conjugacy problem as well as a restricted version of the simultaneous conjugacy problem can be solved in polynomial time even if input words are represented in a compressed form. As a consequence it follows that the word problem for the outer automorphism group of a graph group can be solved in polynomial time.