| OK, that sounds a lot more reasonable. I'm assuming you are working on solving some NP-hard problem? > And if it's not in P, I think it will be very useful to understand WHY it is not; [...] Yes, that's a good approach! Btw, I spent quite a few years on and off trying to resolve the following question https://cstheory.stackexchange.com/questions/41251/simulate-... "Can you 'simulate' a heap in linear time?" I would have been equally happy to find an algorithm that works in linear time, or to prove that it's not possible. Last year I finally found the linear time algorithm. > AFAICT my approach is novel, but if some expert genuinely wants to help me understand where it is not novel, I will gladly explain how it works. I'd be happy to take a look. |
Yes, my choice of the problem is 2XSAT, which is a SAT class whose instances have clauses from 2-SAT and XORSAT. I proved (and I think that's where it becomes novel) that this class is NP-complete. This leads me to believe there is a clever generalization of polynomial algorithms for 2-SAT and XORSAT, and that's the subject of my interest.
The trouble is, algorithms for 2-SAT and XORSAT are wildly different. My first attempt to unify them, half a year ago, has failed. Since then I have made a lot of progress on the theory; now I have another candidate algorithm which generalizes them, and I am about to test it.
> Yes, that's a good approach!
I know, but it gets even better. I roughly follow what Krom did with 2-SAT in 1967. And it turns out, even if your attempt at polynomial algorithm turns out to be incorrect, the character of the exponential blow-up gives you at least some hint of what you need to fix.
> I'd be happy to take a look.
I wish I had written more on it, but the research got priority. For two months now, I am sitting on blogpost draft that outlines 2/3 of my strategy, as well as half of a proper paper; I was waiting if I can somehow conclude with a candidate algorithm, but I don't really have yet that written down in a formal way (it's new so some understanding needs to happen). I'll probably publish the blogpost as it is, and the actual algorithm (if the test implementation works out reasonably well) later as another blogpost. If you're still interested, I will send you an email when I publish the first part, probably this weekend, and you can tell me what you think.