Well, I think you were right to try, in that you learnt a lot about it. And you probably *could* have gone on to do it, if it had been a reasonable thing to do.

Do you think there could be any short cut solution? Something that in practice works more like the recursive algorithm, but that you can put some really large theoretical limit on by proving it the bad cases are ruled out by the proof??

Or you could implement this algorithm, but for graphs with N smaller than [BIGNUM] reduce to the recursive algorithm, instead. That's linear, and leaving out the quadratic algorithm is a bug that will never show up :)

Or you could release it untested, and check the answer, and if it fails automatically email a submission of the core dump to a maths journal of your choice ;)