A quadratic algorithm for road coloring
Data Structures and Algorithms
2013-05-31 v9 Discrete Mathematics
Abstract
The Road Coloring Theorem states that every aperiodic directed graph with constant out-degree has a synchronized coloring. This theorem had been conjectured during many years as the Road Coloring Problem before being settled by A. Trahtman. Trahtman's proof leads to an algorithm that finds a synchronized labeling with a cubic worst-case time complexity. We show a variant of his construction with a worst-case complexity which is quadratic in time and linear in space. We also extend the Road Coloring Theorem to the periodic case.
Cite
@article{arxiv.0803.0726,
title = {A quadratic algorithm for road coloring},
author = {Marie-Pierre Béal and Dominique Perrin},
journal= {arXiv preprint arXiv:0803.0726},
year = {2013}
}