Reference Work Entry

Encyclopedia of Algorithms

pp 644-647

# Perfect Phylogeny (Bounded Number of States)

1997; Kannan, Warnow
• Jesper JanssonAffiliated withOchanomizu University

## Keywords and Synonyms

Compatibility of characters with a bounded number of states; Convex tree-realization of partitions containing a bounded number of sets

## Problem Definition

Let $${ S = \{s_1,s_2,\dots,s_n\} }$$ be a set of elements called objects and species, and let $${ C = \{c_1,c_2,\dots,c_m\} }$$ be a set of functions called characters such that each $${ c_j \in C }$$ is a function from S to the set $${ \{0,1,\dots,r_{j} - 1\} }$$ for some integer rj. For every $${ c_j \in C }$$, the set $${ \{0,1,\dots,r_{j} - 1\} }$$ is called the set of allowed states of character cj, and for any $${ s_i \in S }$$ and $${ c_j \in C }$$, it is said that the state of sion cj is α, or that the state of cjfor si is α, where $${ \alpha = c_j(s_i) }$$. The character state matrix for S and C is the $${ (n \times m) }$$-matrix in which entry (i, j) for any ...

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