Full agreement on my side. Just a couple of comments:

• The OP did add some comment to the thread today, so at least s/he is reading it.
• Providing a polynomial algorithm to one particular NP complete problem is proof for P=NP and the price is yours. Caveat is that most believe, but cannot prove, that P <> NP.
• Approximate solutions are of high value, no question! A large part of our economy runs on them.
• I have and had no intention to belittle your proposed solutions. Just the opposite: I learnt a lot from studying your code.
• Besides the practical application of solutions produced here in the monastery, a bit of pure science should be allowed as well. Even if only for the intellectual challenge and not for any practical use. These kind of discussions seem to have a tendency to drift away from the original question.

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