Sorting networks: To the end and back again

New properties of the front and back ends of sorting networks are studied, illustrating their utility when searching for bounds on optimal networks. Search focuses first on the "out-sides" of the network and then on the inner part. Previous works focused on properties of the front end to break symmetries in the search. The new, out-side-in, properties shed understanding on how sorting networks sort, and facilitate the computation of new bounds on optimality. We present new, faster, parallel sorting networks for 17-20 inputs. For 17 inputs, we show that no sorting network using less layers exists.