论文信息 - A note on diameters of point sets

A note on diameters of point sets

Relationships between the diameter of a set of n points in the plane at mutual distance at least one, the diameter of an equilateral n-gon and the radius of a circle including n unit disks are explored. Upper bounds on the minimal diameter of a point set at mutual distance at least one are presented for up to 30 points.

[1] Michael J. Mossingho. An Isodiametric Problem for Equilateral Polygons , 2008 .

[2] K. Reinhardt. Extremale Polygone gegebenen Durchmessers. , 1922 .

[3] Pierre Hansen,et al. The minimum diameter octagon with unit-length sides: Vincze's wife's octagon is suboptimal , 2003, J. Comb. Theory, Ser. A.

[4] Charles Audet,et al. Nonsmooth optimization through Mesh Adaptive Direct Search and Variable Neighborhood Search , 2006, J. Glob. Optim..

[5] Pierre Hansen,et al. Extremal problems for convex polygons , 2005, J. Glob. Optim..

[6] P. Erdös,et al. Geometrical Extrema Suggested by a Lemma of Besicovitch , 1951 .

[7] Charles Audet,et al. OrthoMADS: A Deterministic MADS Instance with Orthogonal Directions , 2008, SIAM J. Optim..

[8] Pierre Hansen,et al. A branch and cut algorithm for nonconvex quadratically constrained quadratic programming , 1997, Math. Program..

[9] Kenneth Falconer,et al. Unsolved Problems In Geometry , 1991 .

[10] Ferenc Fodor,et al. Minimal Diameter of Certain Sets in the Plane , 1999, J. Comb. Theory, Ser. A.

[11] Pierre Hansen,et al. Extremal Problems for Convex Polygons - An Update , 2007 .