Closest Substring

Keywords and Synonyms

Common approximate substring        

Problem Definition

Closest Substring is a core problem in the field of consensus string analysis with, in particular, applications in computational biology. Its decision version is defined as follows.

Closest Substring

Input: k strings ${ s_1, s_2, \dots , s_k }$ over alphabet Σ and non-negative integers d and L.

Question: Is there a string s of length L and, for all ${ i = 1, \dots, k }$, a length-L substring ${ s^{\prime}_i }$ of s _i such that ${ d_H(s,s^{\prime}_i)\leq d }$?

Here ${ d_H(s, s_i^{\prime}) }$ denotes the Hamming distance between s and s _i ′, i. e., the number of positions in which s and s _i ′ differ. Following the notation used in [7], m is used to denote the average length of the input strings and n to denote the total size of the problem input.

The optimization version of Closest Substring asks for the minimum value of the distance parameter d for which the input strings still allow a solution.

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