An alternate description for ribbon disk complements in the $4$-ball is provided. It is known (and reestablished) that this description is equivalent to the standard LOT description, up to $3$-deformation. Amenable to geometric arguments, the alternate description yields asphericity results for ribbon disk complements using simple graph-theoretic criteria and, later, using a relative homotopy group which arises naturally. In the course of making and modifying the description, two algorithms are given for presenting ribbon disk groups.
"Asphericity results for ribbon disk complements via alternate descriptions." Osaka J. Math. 48 (1) 99 - 125, March 2011.