  We introduce new types of local algorithms, which we call "ASI Algorithms",
and use them to demonstrate a link between descriptive and computable
combinatorics. This allows us to unify arguments from the two fields, and also
sometimes to port arguments from one field to the other. As an example, we
generalize a computable combinatorics result of Kierstead and use it to get
within one color of the Baire measurable analogue of Vizing's Theorem. We also
improve Kierstead's result for multigraphs along the way.
