%0 Journal Article
%T A quadratic algorithm for road coloring
%A Marie-Pierre B¨Ļal
%A Dominique Perrin
%J Computer Science
%D 2008
%I arXiv
%X 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.
%U http://arxiv.org/abs/0803.0726v9