Artículos de revistas
Characterization of Extremal Antipodal Polygons
Fecha
2015Registro en:
Graphs and Combinatorics (2015) 31:321–333
DOI: 10.1007/s00373-015-1548-z
Autor
Aichholzer, O.
Caraballo, L. E.
Díaz Báñez, J. M.
Fabila Monroy, R.
Ochoa Delorenzi, Sergio
Nigsch, P.
Institución
Resumen
Let S be a set of 2n points on a circle such that for each point p∈S also its antipodal (mirrored with respect to the circle center) point p′ belongs to S. A polygon P of size n is called antipodal if it consists of precisely one point of each antipodal pair (p,p′) of S. We provide a complete characterization of antipodal polygons which maximize (minimize, respectively) the area among all antipodal polygons of S. Based on this characterization, a simple linear time algorithm is presented for computing extremal antipodal polygons. Moreover, for the generalization of antipodal polygons to higher dimensions we show that a similar characterization does not exist.