On the Algorithmic Lovász Local Lemma and Acyclic Edge Coloring

The algorithm for Lovász Local Lemma by Moser and Tardos gives a constructive way to prove the existence of combinatorial objects that satisfy a system of constraints. We present an alternative probabilistic analysis of the algorithm that does not involve counting witness-trees. We then apply our approach to Acyclic Edge Coloring to obtain a direct probabilistic proof that a graph with maximum degree ∆ has an acyclic proper edge coloring with at most 4.152(∆−1) colors. Although the numeric result we obtain is slightly worse than the best to date bound of 4(∆ − 1), we think this application illustrates how the intricacies of the entropic method previously used for the analysis can be avoided by our approach. Contact: [email protected], [email protected], [email protected], [email protected] Research co-financed by the European Union (European Social Fund ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF) Research Funding Program: ARISTEIA II.