## Abstract

The problem of aligning two sequences A and B to determine their similarity is one of the fundamental problems in pattern matching. A challenging, basic variation of the sequence similarity problem is the incremental string comparison problem, denoted Consecutive Suffix Alignment, which is, given two strings A and B, to compute the alignment solution of each suffix of A versus B. Here, we present two solutions to the Consecutive Suffix Alignment Problem under the LCS (Longest Common Subsequence) metric, where the LCS metric measures the subsequence of maximal length common to A and B. The first solution is an O (n L) time and space algorithm for constant alphabets, where the size of the compared strings is O (n) and L ≤ n denotes the size of the LCS of A and B. The second solution is an O (n L + n log | Σ |) time and O (n) space algorithm for general alphabets, where Σ denotes the alphabet of the compared strings.

Original language | English |
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Pages (from-to) | 1095-1117 |

Number of pages | 23 |

Journal | Journal of Computer and System Sciences |

Volume | 73 |

Issue number | 7 |

DOIs | |

State | Published - Nov 2007 |

### Bibliographical note

Funding Information:* Corresponding author. Fax: +972 4 824 9331. E-mail addresses: landau@poly.edu (G.M. Landau), gene@eecs.berkeley.edu (E. Myers), michalz@cs.technion.ac.il (M. Ziv-Ukelson). 1 Partially supported by NSF grant CCR-0104307, and by the Israel Science Foundation grants 282/01 and 35/05. 2 Fax: +510 643 8443. 3 Partially supported by the Aly Kaufman Post Doctoral Fellowship and by the Bar-Nir Bergreen Software Technology Center of Excellence.

## Keywords

- Dynamic programming
- Incremental algorithms
- Longest common subsequence
- Match point arithmetic

## ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Networks and Communications
- Computational Theory and Mathematics
- Applied Mathematics