### Abstract

We consider the longest common subsequence (LCS) problem with the restriction that the common subsequence is required to consist of at least k length substrings. First, we show an O(mn) time algorithm for the problem which gives a better worst-case running time than existing algorithms, where m and n are lengths of the input strings. Furthermore, we mainly consider the LCS in at least k length order-isomorphic substrings problem. We show that the problem can also be solved in O(mn) worst-case time by an easy-to-implement algorithm.

Original language | English |
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Title of host publication | SOFSEM 2017 |

Subtitle of host publication | Theory and Practice of Computer Science - 43rd International Conference on Current Trends in Theory and Practice of Computer Science, Proceedings |

Editors | Christel Baier, Mark van den Brand, Johann Eder, Mike Hinchey, Tiziana Margaria, Bernhard Steffen |

Publisher | Springer Verlag |

Pages | 363-374 |

Number of pages | 12 |

ISBN (Print) | 9783319519623 |

DOIs | |

Publication status | Published - 2017 Jan 1 |

Event | 43rd Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2017 - Limerick, Ireland Duration: 2017 Jan 16 → 2017 Jan 20 |

### 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 | 10139 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 43rd Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2017 |
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Country | Ireland |

City | Limerick |

Period | 17/1/16 → 17/1/20 |

### Keywords

- Dynamic programming
- Longest common subsequence
- Order-isomorphism
- Order-preserving matching

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*SOFSEM 2017: Theory and Practice of Computer Science - 43rd International Conference on Current Trends in Theory and Practice of Computer Science, Proceedings*(pp. 363-374). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10139 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-51963-0_28