### Abstract

The convolution between a text string S of length N and a pattern string P of length m can be computed in Ο(N logm) time by FFT. It is known that various types of approximate string matching problems are reducible to convolution. In this paper, we assume that the input text string is given in a compressed form, as a straight-line program (SLP), which is a context free grammar in the Chomsky normal form that derives a single string. Given an SLP S of size n describing a text S of length N, and an uncompressed pattern P of length m, we present a simple Ο(nmlogm)-time algorithm to compute the convolution between S and P. We then show that this can be improved to Ο(min{nm,N - α} logm) time, where α ≥ 0 is a value that represents the amount of redundancy that the SLP captures with respect to the length-m substrings. The key of the improvement is our new algorithm that computes the convolution between a trie of size r and a pattern string P of length m in Ο(r logm) time.

Original language | English |
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Title of host publication | Proceedings - DCC 2013 |

Subtitle of host publication | 2013 Data Compression Conference |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 451-460 |

Number of pages | 10 |

ISBN (Print) | 9780769549651 |

DOIs | |

Publication status | Published - Jan 1 2013 |

Event | 2013 Data Compression Conference, DCC 2013 - Snowbird, UT, United States Duration: Mar 20 2013 → Mar 22 2013 |

### Publication series

Name | Data Compression Conference Proceedings |
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ISSN (Print) | 1068-0314 |

### Other

Other | 2013 Data Compression Conference, DCC 2013 |
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Country | United States |

City | Snowbird, UT |

Period | 3/20/13 → 3/22/13 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Computer Networks and Communications

### Cite this

*Proceedings - DCC 2013: 2013 Data Compression Conference*(pp. 451-460). [6543081] (Data Compression Conference Proceedings). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/DCC.2013.53