Reference Work Entry

Encyclopedia of Algorithms

pp 1-99

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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