n faces. Our algorithm generates each based rectangular drawing having exactly n faces in 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." />


Constant Time Generation of Rectangular Drawings with Exactly n Faces

Satoshi YOSHII  Daisuke CHIGIRA  Katsuhisa YAMANAKA  Shin-ichi NAKANO  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E89-A   No.9   pp.2445-2450
Publication Date: 2006/09/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e89-a.9.2445
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Algorithms and Data Structures
Keyword: 
graphs,  rectangular drawings,  enumeration,  

Full Text: PDF(144.2KB)
>>Buy this Article


Summary: 
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 on 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 in 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 in 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.