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Alex Rivera
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Given an NxNxN binary array (containing only 0's or 1's), how can we obtain the largest cuboid with a non-trivial solution i.e. in O(N^3) ? -- It is the same problem that Find largest rectangle containing only zeros in an N×N binary matrix but in an upper dimension. Also, in my case, the largest rectangle can "cross the edge" of the array i.e. the space is like a torus for a 2D matrix. For a 2D array, if the entry is : 00111 00111 11000 00000 00111 the solution depicted by 'X' is 00XXX 00XXX 11000 00000 00XXX I've done the computation for a NxN binary array and find a solution for the largest rectangle problem in O(N^2) by following the idea in http://tech-queries.blogspot.de/2011/03/maximum-area-rectangle-in-histogram.html . But I don't know how to apply it for a 3D array. -- Example for a 3x3x3 array where the solution "cross the edge": 111 100 011 111 001 111 011 110 011 the solution should be: 1XX 100 0XX 1XX 001 1XX 0XX 110 0XX
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