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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