publication . Preprint . 2020

Compaction for two models of logarithmic-depth trees: Analysis and Experiments

Bodini, Olivier; Genitrini, Antoine; Gittenberger, Bernhard; Larcher, Isabella; Naima, Mehdi;
Open Access English
  • Published: 26 May 2020
Abstract
In this paper we are interested in the quantitative analysis of the compaction ratio for two classical families of trees: recursive trees and plane binary increasing tree. These families are typical representatives of tree models with a small depth. More formally, asymptotically, for a random tree with $n$ nodes, its depth is of order $\log n$. 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 $O(n / \log n)$ nodes. This result must be compared to classical results of compaction in the families of simply generated trees, where the analog result states that the compac...
Subjects
free text keywords: Mathematics - Combinatorics, Computer Science - Data Structures and Algorithms
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