Is there a algorithm that will find as long as possible hamiltonian cycles in v^2 time. I am running a program that needs to find cycles on a sparse graph (4v edges at maximum), and according to my calculations, I need v^2 or better. I understand that to operate in v^2 it would have to be heuristical, and possibly not very accurate. Please tell me if this is impossible, as I have no clue whether this is possible.
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