Is the GAP (graph accessibility problem) NP-Complete ? It has polynomial and non-deterministic polynomial algorithms that solve it, but I don't think this is a criteria that overrides the basic way of showing it's NP-Complete, by showing it is NP and NP-Hard => NP-Complete. I heard both versions from older students than me. So in the end, is it or not NP-Complete?
Is GAP (graph accessibility) NP-Complete?
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Wikipedia says that the problem is
NL-Complete, which means that it’s also inP. This makes it extremely unlikely that it isNP-Complete. If it was, that would prove that P=NP, which is a very old and unsolved question. And it is widely assumed thatP≠NP.You won’t be able to prove that it is not
NP-Completeeither, because that would proveP≠NP.If you can prove that it is
NP-Completeor that it is notNP-Complete, you will recieve an award of one million dollars.So in summary the answer is: It seems very unlikely, but it is just as unlikely that you can prove anything in that direction :).