1. One or more computer storage media including computer executable instructions embodied thereon that, when executed by one or more computing devices, cause the one or more computing devices to perform a method for generating instructions for filling a predetermined region, the method comprising: receiving a dithered specification for the predetermined region; generating a lattice corresponding to the dithered specification, wherein the lattice is populated with a set of vertices, a set of edges connecting the vertices, and cost function data associated with the edges on-the-fly; recursively performing an overlapping divide-and-conquer beam search on the lattice to determine a path through a subset of vertices included in the lattice that minimizes an overall cost of filling the predetermined region, wherein the overall cost is calculated from the cost function data associated with the edges that connect the subset of vertices; and outputting instructions to a processor for the placement of building blocks in the predetermined region, the instructions generated using the determined path.