Constant time generation of free trees
SIAM Journal on Computing
Efficient algorithms for listing combinatorial structures
Efficient algorithms for listing combinatorial structures
Isomorph-free exhaustive generation
Journal of Algorithms
Efficient Generation of Plane Triangulations without Repetitions
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Linear time algorithm for isomorphism of planar graphs (Preliminary Report)
STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
On the effective enumerability of NP problems
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
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A "rooted" plane triangulation is a plane triangulation with one designated vertex on the outer face. In this paper we give a simple algorithm to generate all triconnected rooted plane triangulations with at most n vertices. The algorithm uses O(n) space and generates such triangulations in O(1) time per triangulation without duplications. The algorithm does not output entire triangulations but the difference from the previous triangulation. By modifying the algorithm we can generate all triconnected rooted plane triangulation having exactly n vertices including exactly r vertices on the outer face in O(r) time per triangulation without duplications, while the previous best algorithm generates such triangulations in O(n2) time per triangulation. Also we can generate without duplications all triconnected (non-rooted) plane triangulations having exactly n vertices including exactly r vertices on the outer face in O(r2n) time per triangulation, and all maximal planar graphs in O(n3) time per graph.