I'm a tad suspicious: are the circle packings on Friedman's page proved to be maximal, or are they merely the best known so far? There is no link to any proofs, or key to diameters ... WFL On 2/19/16, rwg <rwg@sdf.org> wrote:
On 2016-02-18 21:01, rwg wrote:
On 2016-02-17 07:01, James Propp wrote:
Does anyone have a favorite example of a fake optimum?
One class of examples that comes to mind is certain packing problems, where the constraints all obey some sort of symmetry but the optimal symmetrical solution is not as good as the optimal asymmetrical solution.
I'm especially interested in optimization problems where a greedy approach seems intuitively optimal but isn't. E.g., try to construct the biggest possible subset of {1,2,...,20} in which no two elements differ by 3 or 5. A greedy construction gives {1,2,3,9,10,11,17,18,19}, but this isn't optimal.
(Yes, this is for my blog. My default is to give credit to contributors, so if you prefer anonymity, please let me know!)
Jim
How many unit diameter pennies fit in a 2x100 rectangle?
Sorry! I meant 2 by 200 rectangle!
And this one amazes me: http://www2.stetson.edu/~efriedma/cirRcir/ Why isn't #31 just #32 symmetrized, with the big purple reduced to a green, and the bottom orange deleted? --rwg
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