You seem to start your argument with

“The argument reduces the minimum-length rectangular partition problem to Planar 3-SAT.”

Shouldn’t this be

reduces Planar 3-SAT to the minimum-length rectangular partition problem?

which is programmed to construct a complete eye anywhere on the body of a living organism that has eyes. I am sure that mathematics has a part in the program that constructs a complete eye that can see.

Reference the discovery of Dr. Walter Gehring of Switzerland.

]]>Thank you for your reply. Well, I mean a 2D array (a matrix) or a 2d rectangle. A very simple polygon.

Thanks again for your reply

]]>Sorry for the delay in responding to you; I’ve been away from the blog for a bit. I’m not yet sure what you mean by a matrix (grid)? Do you mean a geometric object like a grid graph?

]]>I was also looking for this paper. But I am still not quite sure if this might help me in my current problem, I am looking for a way to partition a matrix (grid) into rectangles .. such that they all have minimum edge length. Does this O(n^4) solve this problem?

Thanks again.

]]>Take the given database of structures and run a standard energy minimization algorithm starting with the structures in the database. Unlike attempts to solve for molecular structure by brute force this can be done fairly cheaply since we only look for the nearest local minimum and don’t bother trying to tunnel across higher energy solutions to find a lower absolute minimum.

Since the molecular structure database, in order to provide correct results to it’s users, must provide structures very similar to those taken by the molecules in the real world and such real world structures always occupy a local energy minimum the results of our computations surely compute the structures at least as well as the original dataset.

Moreover, since local energy minimization algorithms should be independent of initial state as long as that state is close to the computed energy minimum our output data would necessarily be indistinguishable from a run of the same program starting on any other nearly correct database of molecular structures.

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