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Constant Time Generation of Rectangular Drawings with Exactly n Faces
Satoshi YOSHII Daisuke CHIGIRA Katsuhisa YAMANAKA Shinichi NAKANO
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E89A
No.9
pp.24452450 Publication Date: 2006/09/01
Online ISSN: 17451337
DOI: 10.1093/ietfec/e89a.9.2445
Print ISSN: 09168508 Type of Manuscript: LETTER Category: Algorithms and Data Structures Keyword: graphs, rectangular drawings, enumeration,
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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.

