In this talk I will report on results of two papers. The first describes an affine analog of Robinson-Schensted correspondence, illuminating the cellular structure in affine type A Kazhdan-Lusztig theory. The second applies the results of the first to understand the structure of undirected edges in the corresponding W-graphs. Equivalently, it builds affine analogs of dual equivalence graphs, distinct from analogs motivated by Schubert calculus. This is a joint work with Michael Chmutov, Elena Yudovina and Joel Lewis.