Data structures: form and function
Data structures: form and function
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
Generation of Binary Trees from Ballot Sequences
Journal of the ACM (JACM)
On the Generation of Binary Trees
Journal of the ACM (JACM)
A Note on Enumerating Binary Trees
Journal of the ACM (JACM)
A numbering system for binary trees
Communications of the ACM
Transformations between tree permutations and inversion tables
CSC '90 Proceedings of the 1990 ACM annual conference on Cooperation
Generating t-ary trees in parallel
Nordic Journal of Computing
On Parallel Generation of t-Ary Trees in an Associative Model
PPAM '01 Proceedings of the th International Conference on Parallel Processing and Applied Mathematics-Revised Papers
A simple optimal representation for balanced parentheses
Theoretical Computer Science
Generating random binary trees - A survey
Information Sciences: an International Journal
Sal/Svm: an assembly language and virtual machine for computing with non-enumerated sets
Virtual Machines and Intermediate Languages
Engineering the LOUDS succinct tree representation
WEA'06 Proceedings of the 5th international conference on Experimental Algorithms
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Let B(N) denote the set of all binary trees that have N nodes. A procedure for randomly generating the trees in B(N) such that each tree is equally likely to occur, that is an unbiased random generator, is given which runs in O(N) time, requires very little storage, and uses a system of arithmetic no larger than is required to represent the number U itself. Previous unbiased random binary tree generators, based on inverse rank functions, ran in O(N log N) time and required multiple precision arithmetic capable of handling numbers of the order of magnitude of the cardinality of B(N).