Physical Sciences and Mathematics Commons^™

The Structure Of Optimal Partitions Of Orthogonal Polygons Into Fat Rectangles, Joseph O'Rourke, Geetika Tewari

Computer Science: Faculty Publications

Motivated by a VLSI masking problem, we explore partitions of an orthogonal polygon of n vertices into isothetic rectangles that maximize the shortest rectangle side over all rectangles. Thus no rectangle is "thin"; all rectangles are "fat". We show that such partitions have a rich structure, more complex than what one might at first expect. For example, for partitions all "cuts" of which are anchored on the boundary, sometimes cuts are needed 1/2 or 1/3 of the distance between two polygon edges, but they are never needed at fractions with a larger denominator. Partitions using cuts without any restrictions seem …