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Glad you found the post useful. Concluding P = NP might be tricky because in real life the input instances may be large. For eg even if S = {10Million, 10Million+1, 10Million+2} and t = {10Million+3}, the pseudo polynomial might take inordinate amount of time while brute force works fast. The converse might hold true for other problems. But on the other hand, a significant number of practical problems can indeed be solved efficiently by decent heuristics. I would also suggest you to take a look at approximation and randomization algorithms as they an orthogonal approach to solving NP-hard problems.

]]>One thing I was thinking about is weak NP-Complete problems. Doesn’t the very distinction seem to hint that P might be equal to NP? I mean, that a significant part of NP-Complete problems do admit pseudo polynomial algorithms makes it seem that there is still more to explore when talking about alternate, more efficient ways to deal with certain problems and their constraints.

I should remember to follow up on this thought and study more!

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