Rectilinear Steiner trees on a checkerboard

The rectilinear Steiner tree problem is to find a minimum-length set of horizontal and vertical line segments that interconnect a given set of points in the plane. Here we study the thumbnail rectilinear Steiner tree problem, where the input points are drawn from a small integer grid. Specifically, we devise a fully-set decomposition algorithm for computing optimal thumbnail rectilinear Steiner trees. We then present experimental results comparing the performance of this algorithm with two existing algorithms for computing optimal rectilinear Steiner trees. The thumbnail rectilinear Steiner tree problem has applications in VLSI placement algorithms, based on geometric partitioning, global routing of field-programmable gate arrays, and routing estimation during floorplanning.