A Fast Algorithm for Stallings' Folding Process
Nicholas Wembley Matheson Touikan
TL;DR
This paper introduces a highly efficient algorithm for Stallings' folding process that significantly reduces the computational complexity for fixed free groups and arbitrary finitely generated subgroups.
Contribution
The paper presents a novel algorithm achieving O(N log^*(N)) time complexity for Stallings' folding process, improving over previous methods.
Findings
Folding process runs in near-linear time for fixed free groups.
Algorithm efficiency is demonstrated for arbitrary finitely generated subgroups.
Complexity analysis confirms the theoretical improvement over existing algorithms.
Abstract
We show that for a fixed free group F and an arbitrary finitely generated subgroup H (as given above) we can perform the Stalling's folding process in time O(N log^*(N)), where N is the sum of the word lengths of the given generators of H.
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