treebalance (version 1.2.0)

furnasI: Calculation of the Furnas rank for rooted binary trees

Description

This function calculates the Furnas rank \(F(T)\) for a given rooted binary tree \(T\). \(F(T)\) is the unique rank of the tree \(T\) among all rooted binary trees with \(n\) leaves in the left-light rooted ordering. For details on the left-light rooted ordering as well as details on how the Furnas rank is computed, see "The generation of random, binary unordered trees" by G.W. Furnas (1984) or "Tree balance indices: a comprehensive survey" by Fischer et al. (2023). The Furnas rank is a balance index.

The concept of assigning each rooted binary tree a unique tuple \((rank, n)\) allows to store many trees with minimal storage use.

For details on the Furnas rank, see also Chapter 22 in "Tree balance indices: a comprehensive survey" (https://doi.org/10.1007/978-3-031-39800-1_22).

Usage

furnasI(tree)

Value

furnasI returns the unique Furnas rank of the given tree, i.e. the rank of the tree among all rooted binary trees with \(n\) leaves in the left-light rooted ordering. Since the values can get quite large, the function returns them in \(big.z\) format (package \(gmp\)).

Arguments

tree

A rooted binary tree in phylo format.

Author

Luise Kuehn, Lina Herbst

References

G. W. Furnas. The generation of random, binary unordered trees. Journal of Classification, 1984. doi: 10.1007/bf01890123. URL https://doi.org/10.1007/bf01890123.

M. Kirkpatrick and M. Slatkin. Searching for evolutionary patterns in the shape of a phylogenetic tree. Evolution, 1993. doi: 10.1111/j.1558-5646.1993.tb02144.x.

Examples

tree <- ape::read.tree(text="((((,),),(,)),(((,),),(,)));")
furnasI(tree)