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Compaction for two models of logarithmic‐depth trees: Analysis and experiments
Author(s) -
Bodini Olivier,
Genitrini Antoine,
Gittenberger Bernhard,
Larcher Isabella,
Naima Mehdi
Publication year - 2022
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/rsa.21056
Subject(s) - logarithm , binary tree , compaction , binary number , random binary tree , plane (geometry) , binary search tree , tree (set theory) , mathematics , ternary search tree , graph , combinatorics , algorithm , computer science , geometry , tree structure , interval tree , mathematical analysis , geology , arithmetic , geotechnical engineering
We are interested in the quantitative analysis of the compaction ratio for two classical families of trees: recursive trees and plane binary increasing trees. These families are typical representatives of tree models with a small depth. Once a tree of size n is compacted by keeping only one occurrence of all fringe subtrees appearing in the tree the resulting graph contains only O ( n / ln n ) nodes. This result must be compared to classical results of compaction in the families of simply generated trees, where the analogous result states that the compacted structure is of size of order n / ln n. The result about the plane binary increasing trees has already been proved, but we propose a new and generic approach to get the result. Finally, an experimental study is presented, based on a prototype implementation of compacted binary search trees that are modeled by plane binary increasing trees.