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Asymmetric polygons with maximum area

Author

Listed:
  • Barba, L.
  • Caraballo, L.E.
  • Díaz-Báñez, J.M.
  • Fabila-Monroy, R.
  • Pérez-Castillo, E.

Abstract

We say that a polygon inscribed in the circle is asymmetric if it contains no two antipodal points being the endpoints of a diameter. Given n diameters of a circle and a positive integer k < n, this paper addresses the problem of computing a maximum area asymmetric k-gon having as vertices k < n endpoints of the given diameters. The study of this type of polygons is motivated by ethnomusiciological applications.

Suggested Citation

  • Barba, L. & Caraballo, L.E. & Díaz-Báñez, J.M. & Fabila-Monroy, R. & Pérez-Castillo, E., 2016. "Asymmetric polygons with maximum area," European Journal of Operational Research, Elsevier, vol. 248(3), pages 1123-1131.
    • Handle: RePEc:eee:ejores:v:248:y:2016:i:3:p:1123-1131
    DOI: 10.1016/j.ejor.2015.08.013
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    References listed on IDEAS

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    1. Schell, Daniel, 2002. "Optimality in musical melodies and harmonic progressions: The travelling musician," European Journal of Operational Research, Elsevier, vol. 140(2), pages 354-372, July.
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    Cited by:

    1. Caraballo, L.E. & Díaz-Báñez, J.M. & Rodríguez, F. & Sánchez-Canales, V. & Ventura, I., 2022. "Scaling and compressing melodies using geometric similarity measures," Applied Mathematics and Computation, Elsevier, vol. 426(C).
    2. Bereg, Sergey & Díaz-Báñez, José-Miguel & Kroher, Nadine & Ventura, Inmaculada, 2019. "Computing melodic templates in oral music traditions," Applied Mathematics and Computation, Elsevier, vol. 344, pages 219-229.

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