Reference Work Entry

Encyclopedia of Algorithms

pp 651-653

# Phylogenetic Tree Construction from a Distance Matrix

1989; Hein
• Jesper JanssonAffiliated withOchanomizu University

## Keywords and Synonyms

Phylogenetic tree construction from a dissimilarity matrix

## Problem Definition

Let n be a positive integer. A distance matrix of order n (also called a dissimilarity matrix of order n) is a matrix D of size $${ (n \times n) }$$ which satisfies: (1) $${ D_{i,j} > 0 }$$ for all $${ i,j \in \{1,2,\dots,n\} }$$ with $${ i \neq j }$$; (2) $${ D_{i,j} = 0 }$$ for all $${ i,j \in \{1,2,\dots,n\} }$$ with $${ i = j }$$; and (3) $${ D_{i,j} = D_{j,i} }$$ for all $${ i,j \in \{1,2,\dots,n\} }$$.

Below, all trees are assumed to be unrooted and edge-weighted. For any tree $${ \mathcal{T} }$$, the distance between two nodes u and v in $${ \mathcal{T} }$$ is defined as the sum of the weights of all edges on the unique path in $${ \mathcal{T} }$$ between u and v, and is denoted by $${ d_{u,v}^{\mathcal{T}} }$$. A tree  ...

This is an excerpt from the content