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) |
|---|---|
| State | Published - Dec 1 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 |
|---|---|
| Country | Canada |
| City | Toronto, ON |
| Period | 8/10/11 → 8/12/11 |
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ASJC Scopus subject areas
- Computational Mathematics
- Geometry and Topology
Cite this
Minimum many-to-many matchings for computing the distance between two sequences. / Mohamad, Mustafa; Rappaport, David; Toussaint, Godfried.
2011. Paper presented at 23rd Annual Canadian Conference on Computational Geometry, CCCG 2011, Toronto, ON, Canada.Research output: Contribution to conference › Paper
}
TY - CONF
T1 - Minimum many-to-many matchings for computing the distance between two sequences
AU - Mohamad, Mustafa
AU - Rappaport, David
AU - Toussaint, Godfried
PY - 2011/12/1
Y1 - 2011/12/1
N2 - 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.
AB - 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.
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