Holonomic equations and efficient random generation of binary trees

Holonomic equations are recursive equations which allow computing efficiently numbers of combinatoric objects. Rémy showed that the holonomic equation associated with binary trees yields an efficient linear random generator of binary trees. I extend this paradigm to Motzkin trees and Schröder trees...

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Bibliographic Details
Published in:Discrete mathematics and theoretical computer science Vol. 25:2; no. 2; pp. 1 - 27
Main Author: Lescanne, Pierre
Format: Journal Article
Language:English
Published: Nancy DMTCS 01.01.2023
Discrete Mathematics & Theoretical Computer Science
Subjects:
[info.info-cc]computer science [cs]/computational complexity [cs.cc]
[info.info-ds]computer science [cs]/data structures and algorithms [cs.ds]
Algorithms
binary tree
catalan number
combinatorics
combinatorics random generation motzkin number catalan number binary tree unary-binary tree
Complexity
Computational Complexity
Computer Science
Data Structures and Algorithms
Mathematical analysis
motzkin number
random generation
schroeder number
unary-binary tree
unary-binary tree
binary tree
random generation
Schroeder number
Motzkin number
Catalan number
combinatorics random generation Motzkin number Catalan number binary tree unary-binary tree
combinatorics
ISSN:1365-8050, 1462-7264, 1365-8050
Online Access:Get full text
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Summary:Holonomic equations are recursive equations which allow computing efficiently numbers of combinatoric objects. Rémy showed that the holonomic equation associated with binary trees yields an efficient linear random generator of binary trees. I extend this paradigm to Motzkin trees and Schröder trees and show that despite slight differences my algorithm that generates random Schröder trees has linear expected complexity and my algorithm that generates Motzkin trees is in O(n) expected complexity, only if we can implement a specific oracle with a O(1) complexity. For Motzkin trees, I propose a solution which works well for realistic values (up to size ten millions) and yields an efficient algorithm.
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:1365-8050
1462-7264
1365-8050
DOI:10.46298/dmtcs.10952