For a particular problem, I think I've found a way to solve it by translating it into a 7-dimensional cube. Basically, I'll associate the vertices of the cube with some objects and would have to find the optimal way to arrange them based on the edges between the vertices( say an arrangement with a minimum number of edges).
I need to know the go-to method for solving such problems. I've heard of polymake before. Can I use it for my use? Where can I find more help?
EDIT :The problem
I have eight 7 bit strings (a,b,c,d,e,f,g,h). I think I can find suitable vertices for them in a 7 dimensional cube. Now, I need to find two vertices (X, Y) such that, when we partition the eight strings to two sets and associate the two sets with our two new vertices, the sum of the number of edges connecting the chosen vertices(X, Y) with the strings in their corresponding sets should be a minimum.
For eg. If we partition the eight strings to (a, c, e) and (b, d, f, g, h) and associate X and Y with them respectively, then, the sum would be given by adding the number of edges between X-a, X-c and X-e and Y-b, Y-d, Y-f, Y-g, Y-h. The problem is to find the optimum partition and the optimum choice of vertices such that this sum is minimum.
My vertices are:
00000000010111010110101110101001011101110011001101110001