Minimum many-to-many matchings for computing the distance between two sequences

Mustafa Mohamad, David Rappaport, Godfried Toussaint

Research output: Contribution to conferencePaper

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 languageEnglish (US)
StatePublished - Dec 1 2011
Event23rd Annual Canadian Conference on Computational Geometry, CCCG 2011 - Toronto, ON, Canada
Duration: Aug 10 2011Aug 12 2011

Other

Other23rd Annual Canadian Conference on Computational Geometry, CCCG 2011
CountryCanada
CityToronto, ON
Period8/10/118/12/11

Fingerprint

Many to many
Continuous Optimization
Computing
Chord or secant line
Music
Real Line
Set of points
Optimization Problem
Minimise

ASJC Scopus subject areas

  • Computational Mathematics
  • Geometry and Topology

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.

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 conferencePaper

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, 8/10/11 - 8/12/11, .
Mohamad M, Rappaport D, Toussaint G. Minimum many-to-many matchings for computing the distance between two sequences. 2011. Paper presented at 23rd Annual Canadian Conference on Computational Geometry, CCCG 2011, Toronto, ON, Canada.
Mohamad, Mustafa ; Rappaport, David ; Toussaint, Godfried. / 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.
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