Perfect Phylogeny (Bounded Number of States)

Years and Authors of Summarized Original Work

• 1994; Agarwala, Fernández-Baca

• 1997; Kannan, Warnow

Problem Definition

Let $S =\{ s_{1},s_{2},\ldots ,s_{n}\}$ be a set of elements called objects and let $C =\{ c_{1},c_{2},\ldots ,c_{m}\}$ be a set of functions called characters such that each c _j ∈ C is a function from S to the set $\{0,1,\ldots ,r_{j} - 1\}$ for some integer r _j . For every c _j ∈ C, the set $\{0,1,\ldots ,r_{j} - 1\}$ is called the set of allowed states of character c _j , and for any s _i ∈ S and c _j ∈ C, it is said that the state of s_ion c_j is α, or that the state of c_jfor s_i is α, where α = c _j (s _i ). The character state matrix for S and C is the (n × m)-matrix in which entry (i, j) for any $i \in \{ 1,2,\ldots ,n\}$ and $j \in \{ 1,2,\ldots ,m\}$ equals the state of s _i on c _j .

Perfect Phylogeny (Bounded Number of States), Fig. 1

(a) An example of a character state matrix M for $S =\{ s_{1},s_{2},\ldots ,s_{6}\}$ and C = { c₁, c₂, c₃} with r₁ = 3, r₂...