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Efficient Generation of Plane Triangulations with a Degree Constraint
Hiroyuki TANAKA Zhangjian LI Shin-ichi NAKANO
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2003/04/01
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section of Selected Papers from the 15th Workshop on Circuits and Systems in Karuizawa)
graph, algorithm, plane graph, generation,
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A "based" plane triangulation is a plane triangulation with one designated edge on the outer face. In this paper we give a simple algorithm to generate all biconnected based plane triangulations with at most n vertices and with maximum degree at most D. The algorithm uses O(n) space and generates such triangulations in O(1) time per triangulation without duplications. The algorithm does not output entire triangulation but the difference from the previous triangulation. By modifying the algorithm we can generate all biconnected based plane triangulations with exactly n vertices and maximum degree at most D in O(1) time per triangulation, and all biconnected (non-based) plane triangulations with exactly n vertices and maximum degree at most D in O(n3) time per triangulation without duplications.