### Abstract

Given a set S of k strings of maximum length n, the goal of the closest substring problem (CSSP) is to find the smallest integer d (and a corresponding string t of length ℓ ≤ n) such that each string s ∈ S has a substring of length ℓ of "distance" at most d to t. The closest string problem (CSP) is a special case of CSSP where ℓ = n. CSP and CSSP arise in many applications in bioinformatics and are extensively studied in the context of Hamming and edit distance. In this paper we consider a recently introduced distance measure, namely the rank distance. First, we show that the CSP and CSSP via rank distance are NP-hard. Then, we present a polynomial time k-approximation algorithm for the CSP problem. Finally, we give a parametrized algorithm for the CSP (the parameter is the number of input strings) if the alphabet is binary and each string has the same number of 0's and 1's.

Original language | English |
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Title of host publication | Combinatorial Pattern Matching - 23rd Annual Symposium, CPM 2012, Proceedings |

Pages | 413-426 |

Number of pages | 14 |

DOIs | |

Publication status | Published - Jul 4 2012 |

Event | 23rd Annual Symposium on Combinatorial Pattern Matching, CPM 2012 - Helsinki, Finland Duration: Jul 3 2012 → Jul 5 2012 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 7354 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 23rd Annual Symposium on Combinatorial Pattern Matching, CPM 2012 |
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Country | Finland |

City | Helsinki |

Period | 7/3/12 → 7/5/12 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Combinatorial Pattern Matching - 23rd Annual Symposium, CPM 2012, Proceedings*(pp. 413-426). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7354 LNCS). https://doi.org/10.1007/978-3-642-31265-6_33