### Abstract

Two algorithms to find the minimum area between two given orthogonal melodies, M_{a} and M_{b}, of size n and m, respectively (n > m) are presented. Both algorithms can be used for cyclic melodies as well as in the context of retrieving short patterns from a database. The algorithms are described for the case where the melodies are cyclic. The first algorithm assumes that the Θ direction is fixed, and it runs in O(n) time. The second algorithm finds the minimum area when both the z and Θ relative positions can be varied. It is proved that it runs in O(nmlogn) time. In each case, it is assumed that the edges defining M_{a} and M_{b} are given in the order in which they appear in melodies. Finally, natural extensions are discussed both for the polygonal description of melodies and for different types of queries.

Original language | English (US) |
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Pages (from-to) | 67-76 |

Number of pages | 10 |

Journal | Computer Music Journal |

Volume | 30 |

Issue number | 3 |

DOIs | |

State | Published - Sep 1 2006 |

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### ASJC Scopus subject areas

- Media Technology
- Music
- Computer Science Applications

### Cite this

*Computer Music Journal*,

*30*(3), 67-76. https://doi.org/10.1162/comj.2006.30.3.67