A Compact Code for Rectangular Drawings with Degree Four Vertices

A rectangular drawing is a partition of a rectangle into a set of rectangles. Rectangular drawings have many important applications including VLSI layout. Since the size of rectangular drawings may be huge, compact encodings are desired. Several compact encodings of rectangular drawings without degree four vertices are known. In this paper, we design two compact encodings for rectangular drawings with degree four vertices. We give 2m = 6f − 2n4 + 6 bits and 5f − 5 bits encodings for rectangular drawings, where m is the number of edges, f is the number of faces, and n4 is the number of vertices with degree four.