  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.
