2014/10/06 by Anton Bernshteyn, Bernshteyn, Anton
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.1410.1591
openalex publication_date 2014/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Lovász Local Lemma is a very powerful tool in probabilistic combinatorics, that is often used to prove existence of combinatorial objects satisfying certain constraints. Moser and Tardos have shown that the LLL gives more than just pure existence results: there is an effective randomized algorithm that can be used to find a desired object. In order to analyze this algorithm Moser and Tardos developed the so-called entropy compression method. It turned out that one could obtain better combinatorial results by a direct application of the entropy compression method rather than simply appealing to the LLL. We provide a general statement that implies both these new results and the LLL itself.