### Abstract

Motivated by a problem in music theory of measuring the distance between chords and scales we consider algo- rithms for obtaining a minimum-weight many-to-many matching between two sets of points on the real line. Given sets A and B, we want to find the best rigid translation of B and a many-to-many matching that minimizes the sum of the squares of the distances be- tween matched points. We provide a discrete algorithm that solves this continuous optimization problem, and discuss other related matters.

Original language | English (US) |
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State | Published - 2011 |

Event | 23rd Annual Canadian Conference on Computational Geometry, CCCG 2011 - Toronto, ON, Canada Duration: Aug 10 2011 → Aug 12 2011 |

### Other

Other | 23rd Annual Canadian Conference on Computational Geometry, CCCG 2011 |
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Country | Canada |

City | Toronto, ON |

Period | 8/10/11 → 8/12/11 |

### ASJC Scopus subject areas

- Computational Mathematics
- Geometry and Topology

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## Cite this

Mohamad, M., Rappaport, D., & Toussaint, G. (2011).

*Minimum many-to-many matchings for computing the distance between two sequences*. Paper presented at 23rd Annual Canadian Conference on Computational Geometry, CCCG 2011, Toronto, ON, Canada.