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  ...

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