The small hexagon and heptagon with maximum sum of distances between vertices |
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| Authors: | Charles Audet Anthony Guillou Pierre Hansen Frédéric Messine Sylvain Perron |
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| Affiliation: | 1.GERAD and école Polytechnique de Montréal,Montreal,Canada;2.HEC Montréal,Montreal,Canada;3.GERAD and HEC Montréal,Montreal,Canada;4.ENSEEIHT-IRIT,Toulouse Cedex 7,France |
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| Abstract: | ![]()
The hexagon and heptagon with unit diameter and maximum sum of Euclidean distances between vertices are determined by enumerating diameter configurations, and by using a branch and cut algorithm for nonconvex quadratic programming. Lower bounds on the value on this sum are presented for polygon with a larger number of vertices. |
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