Substring Parsimony

Years and Authors of Summarized Original Work

• 2001; Blanchette, Schwikowski, Tompa

Problem Definition

The Substring Parsimony Problem, introduced by Blanchette et al. [1] in the context of motif discovery in biological sequences, can be described in a more general framework:  

Input:

• A discrete space ${ \mathcal{S} }$ on which an integral distanced is defined (i.e., ${ d(x,y) \in \mathbb{N} \ \forall x,}$${y \in \mathcal{S} }$ ).

• A rooted binary tree ${ T=(V,E) }$ with n leaves. Vertices are labeled ${ \{1,2, \dots,n,}$${\dots,|V|\} }$, where the leaves are vertices ${ \{1,2, \dots,n\} }$.

• Finite sets ${ S_1,S_2, \dots, S_n }$, where set ${ S_i \subseteq \mathcal{S} }$ is assigned to leaf i, for all ${ i=1 \dots n }$.

• A non-negative integer t

Output: All solutions of the form ${ (x_1,x_2, \dots,}$${x_n, \dots,x_{|V|}) }$ such that:

• ${ x_i \in \mathcal{S} }$ for all ${ i =1 \dots |V| }$

• ${ x_i \in S_i }$ for all \( { i=1 \dots n...