Octagonal drawings of plane graphs with prescribed face areas

Abstract

An orthogonal drawing of a plane graph is called an octagonal drawing if each inner face is drawn as a rectilinear polygon of at most eight (polygonal) vertices and the contour of the outer face is drawn as a rectangle. A slicing graph is obtained from a rectangle by repeatedly slicing it vertically and horizontally. A slicing graph is called a good slicing graph if either the upper subrectangle or the lower one obtained by any horizontal slice will never be vertically sliced, roughly speaking. In this paper we show that every good slicing graph has an octagonal drawing with prescribed face areas, in which the area of each inner face is equal to a prescribed value. Such a drawing has practical applications in VLSI floorplanning. We also give a linear-time algorithm to find such a drawing when a “slicing tree” is given. We furthermore present a sufficient condition for a plane graph to be a good slicing graph.