Efficiently list-edge coloring multigraphs asymptotically optimally

We give polynomial time algorithms for the seminal results of Kahn, who showed that the Goldberg-Seymour and List-Coloring conjectures for (list-)edge coloring multigraphs hold asymptotically. Kahn's arguments are based on the probabilistic method and are non-constructive. Our key insight is to show that the main result of Achlioptas, Iliopoulos and Kolmogorov for analyzing local search algorithms can be used to make constructive applications of a powerful version of the so-called Lopsided Lovasz Local Lemma. In particular, we use it to design algorithms that exploit the fact that correlations in the probability spaces on matchings used by Kahn decay with distance.