Problem 4 on the latest homework turns out to be a lot harder than we anticipated. (Thanks to Jiri and Min for pointing this out).
Here is a modification that makes it much more tractable. The separation penalty between vertices i and j will now depend on the distance between the labels of i and j. That is, label pairs (Bac, Foc) and (Foc, For) still result in penalty p_i,j, but the label pair (Bac,For) now results in penalty 2*p_i,j
Sorry about this. Grading will be lenient, and extra credit if you solve the original problem.
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