Reference Work Entry

Encyclopedia of Algorithms

pp 246-248

# Directed Perfect Phylogeny (Binary Characters)

1991; Gusfield
• Jesper JanssonAffiliated withOchanomizu University

## Keywords and Synonyms

Directed binary character compatibility

## Problem Definition

Let $${ S = \{s_1,s_2,\dots,s_n\} }$$ be a set of elements called objects, and let $${ C = \{c_1,c_2,\dots,c_m\} }$$ be a set of functions from S to $${ \{0,1\} }$$ called characters. For each object $${ s_i \in S }$$ and character $${ c_j \in C }$$, it is said that sihascj if $${ c_j(s_i) = 1 }$$ or that sidoes not havecj if $${ c_j(s_i) = 0 }$$, respectively (in this sense, characters are binary). Then the set S and its relation to C can be naturally represented by a matrix M of size $${ (n \times m) }$$ satisfying $${ M[i,j] = c_j(s_i) }$$ for every $${ i \in \{1,2,\dots,n\} }$$ and $${ j \in \{1,2,\dots,m\} }$$. Such a matrix M is called a binary character state matrix.

Next, for each $$s_i \in S$$, define the set ...

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