Asymmetric polygons with maximum area

Asymmetric polygons with maximum area

•A new extremal problem in operations research is introduced.•The goal is to compute a maximum area k-gon inscribed in a circle with non-antipodal vertices.•We solve the problem efficiently.•The study of this type of polygons is motivated by musiciological applications. We say that a polygon inscrib...

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Bibliographic Details
Published in:European journal of operational research Vol. 248; no. 3; pp. 1123 - 1131
Main Authors: Barba, L., Caraballo, L.E., Díaz-Báñez, J.M., Fabila-Monroy, R., Pérez-Castillo, E.
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01-02-2016
Elsevier Sequoia S.A
Subjects:
Algorithms
Asymmetry
Combinatorial optimization
Computational music theory
Global optimization
Mathematical problems
Musical rhythms
Musicology
Polygons
Studies
Musical rhythms
Global optimization
Algorithms
Computational music theory
Combinatorial optimization
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Summary:•A new extremal problem in operations research is introduced.•The goal is to compute a maximum area k-gon inscribed in a circle with non-antipodal vertices.•We solve the problem efficiently.•The study of this type of polygons is motivated by musiciological applications. 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.
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2015.08.013