Is there some language that is NP-complete but for which we know some "quick" algorithm? I don't mean like the ones for knapsack where we can do well on average, I mean that even in the worst case the runtime is something like 2^n^epsilon, where the result holds for any epsilon>0 and so we can allow it to get arbitrarily close to 0.
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2I was able to determinine that this question was easily googlable homework in O(2^n^0.01) time. – msw May 26 '10 at 15:36
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1@msw: provide a source or roll back, please. – danben May 26 '10 at 15:37
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@danben: I guess the joke was lost on you. – Mike Atlas May 26 '10 at 15:39
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1@Mike Atlas: I guess so; please explain the joke where you tag other people's posts as "homework" without verification. – danben May 26 '10 at 15:42
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Yes, this always bothers me. This seems like it could be a homework question, or it could be someone wondering about something she read. I don't want to do people's homework, but I am happy to satisfy curiosity if I can, and I sometimes learn something too. On the other hand, I sometimes think SO is used as a crutch for those trying to learn a language on their own, but leaving the deep thinking to others. – WhirlWind May 26 '10 at 15:46
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@WhirlWind - generally I will just ask the OP to tag the post themselves if it is in fact homework. This seems to work well - they'll either tag it or say that it isn't, which I think is good enough. The exception is when someone pastes a problem verbatim from their assignment (which is easily identifiable anyway). – danben May 26 '10 at 16:08
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If you do find a "quick" algorithm to this np-complete problem, you just solved that P=NP, and as you know, that is still an open question.
Itsik
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