Directed Perfect Phylogeny (Binary Characters)

Years and Authors of Summarized Original Work

• 1991; Gusfield

• 1995; Agarwala, Fernández-Baca, Slutzki

• 2004; Pe’er, Pupko, Shamir, Sharan

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 from S to {0, 1} called characters. For each object s _i  ∈ S and character c _j  ∈ C, we say that s_i has c_j if c _j (s _i ) = 1 or that s_i does not have c_j 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 × m) satisfying M[i, j] = c _j (s _i ) for every $i \in \{ 1,2,\ldots ,n\}$ and $j \in \{ 1,2,\ldots ,m\}$. Such a matrix M is called a binary character state matrix.

Next, for each s _i  ∈ S, define the set $C_{s_{i}} =\{ c_{j} \in C\, :\, s_{i}\text{ has }c_{j}\}$. A phylogeny for S is a tree whose leaves are bijectively labeled by S, and a directed perfect phylogeny for (S,C)...