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 that we can combine sophisticated techniques due to Achlioptas, Iliopoulos, and Kolmogorov for the analysis of local search algorithms with correlation decay properties of the probability spaces on matchings used by Kahn in order to construct efficient edge-coloring algorithms.