Constant Time Generation of Rectangular Drawings with Exactly n Faces

Abstract

A plane drawing of a plane graph is called a rectangular drawing if every face including the outer face is a rectangle. A based rectangular drawing is a rectangular drawing with a designated base line segment the outer face. An algorithm to generate all based rectangular drawings having exactly n faces is known. The algorithm generates each based rectangular drawing having exactly n faces constant time on average. In this paper, we give another simple algorithm to generate all based rectangular drawings having exactly n faces. Our algorithm generates each based rectangular drawing having exactly n faces constant time in the worst case. Our algorithm generates each based rectangular drawing so that it can be obtained from the preceding one by at most three operations and does not output entire drawings but the difference from the preceding one. Therefore the derived sequence of based rectangular drawings is a kind of combinatorial Gray code for based rectangular drawings.