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arXiv · 0803.0726

A quadratic algorithm for road coloring

Marie-Pierre Béal·Dominique Perrin
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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.

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Marie-Pierre Béal, Dominique Perrin. 2013-05-30. A quadratic algorithm for road coloring. https://arxiv.org/abs/0803.0726

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