Efficient Generation of Plane Triangulations with a Degree Constraint

摘要

A "based" plane triangulation is a plane trian-gulation 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(n~3) time per triangulation without duplications.