## Abstract

Given two strings, X and Y, both of length O(n) over alphabet ∑, a basic problem (local alignment) is to find pairs of similar substrings, one from X and one from Y. For substrings X' and Y' from X and Y, respectively, the metric we use to measure their similarity is normalized alignment value: LCS(X′,Y′)/(|X′|+|Y′|). Given an integer M we consider only those substrings whose LCS length is at least M. We present an algorithm that reports the pairs of substrings with the highest normalized alignment value in O(n log|∑|+r M log log n) time (r-the number of matches between X and Y). We also present an O(n log|∑|+r L log log n) algorithm (L = LCS(X,Y)) that reports all substring pairs with a normalized alignment value above a given threshold.

Original language | English |
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Pages (from-to) | 179-194 |

Number of pages | 16 |

Journal | Algorithmica |

Volume | 43 |

Issue number | 3 |

DOIs | |

State | Published - Sep 2005 |

## Keywords

- Algorithms
- Dynamic programming
- Largest Common Subsequence (LCS)
- Local alignment
- String matching

## ASJC Scopus subject areas

- Computer Science (all)
- Computer Science Applications
- Applied Mathematics