Log In Sign Up

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

by   Olivier Bodini, et al.

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 compacted structure is of size of order n / √(log n). We end the paper with an experimental quantitative study, based on a prototype implementation of compacted binary search trees, that are modeled by plane binary increasing trees.


page 1

page 2

page 3

page 4


Distinct Fringe Subtrees in Random Trees

A fringe subtree of a rooted tree is a subtree induced by one of the ver...

Entropy rates for Horton self-similar trees

In this paper we examine planted binary plane trees. First, we provide a...

Counting embeddings of rooted trees into families of rooted trees

The number of embeddings of a partially ordered set S in a partially ord...

Recursive PGFs for BSTs and DSTs

We review fundamentals underlying binary search trees and digital search...

Clifford algebras, Spin groups and qubit trees

Representations of Spin groups and Clifford algebras derived from struct...

Decomposable Families of Itemsets

The problem of selecting a small, yet high quality subset of patterns fr...

Ranked Schröder Trees

In biology, a phylogenetic tree is a tool to represent the evolutionary ...