Generating rooted and free plane trees

Authors:
Joe Sawada
Affiliations:
University of Guelph, Guelph, Canada
Venue:
ACM Transactions on Algorithms (TALG)
Year:
2006

Citing 7
Cited 2

Constant time generation of free trees

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The advantages of forward thinking in generating rooted and free trees

Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
An Efficient Algorithm for Generating Necklaces with Fixed Density

SIAM Journal on Computing
Fast algorithms to generate necklaces, unlabeled necklaces, and irreducible polynomials over GF(2)

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A Fast Algorithm for Generating Nonisomorphic Chord Diagrams

SIAM Journal on Discrete Mathematics
Efficient generation of plane trees

Information Processing Letters
The On-Line Encyclopedia of Integer Sequences

Calculemus '07 / MKM '07 Proceedings of the 14th symposium on Towards Mechanized Mathematical Assistants: 6th International Conference

Efficient Enumeration of Ordered Trees with k Leaves (Extended Abstract)

WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
Efficient enumeration of ordered trees with k leaves

Theoretical Computer Science

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Abstract

This article has two main results. First, we develop a simple algorithm to list all nonisomorphic rooted plane trees in lexicographic order using a level sequence representation. Then, by selecting a unique centroid to act as the root of a free plane tree, we apply the rooted plane tree algorithm to develop an algorithm to list all nonisomorphic free plane trees. The latter algorithm also uses a level sequence representation and lists all free plane trees with a unique centroid first followed by all free plane trees with two centroids. Both algorithms are proved to run in constant amortized time using straightforward bounding methods.