I'm currently peer-reviewing a paper (for a computer science conference; review is double-blind). While reading it, I came up with a method for the problem they're solving, somewhat inspired by their approach but fairly separate. I haven't implemented and tested it yet, but I expect it to be better than their approach, and it is definitely (in my mind) simpler. The idea came from slightly reframing their approach based on papers that they've cited in their submission, so they had the tools to do so, but they may not be as familiar with as I am (it happens to be right in my wheelhouse).
I see two options here:
Suggest the reframing and the new method to them in the review. They may or may not do anything about it, but if they do, all I get is thanks to an anonymous reviewer in their acknowledgements, assuming the paper gets in. (In my opinion, their paper is probably borderline for this conference.) If they don't use the idea, then it just goes away.
Don't say anything about it in the review; develop the method independently. think, at this early stage, that it's reasonably likely a whole new paper can be written based on this method and related improvements I have in mind. If their paper gets in to this conference, or is put online / gets in somewhere else before I'm done with my paper, cite them. If it doesn't, I could either ignore their paper and write my own – which feels somewhat dishonest, though I wouldn't really be using their results in my new paper – or ask the PC to get me in touch with the authors for possibly collaborating on a single joint paper with both methods. I don't know if that kind of thing is ever done.
Option 1 is clearly ethical, but if option 2 is also ethical, it's both better for my career and possibly better for scientific progress as a whole (if they don't end up using the idea). So my question is: is option 2 okay? What do I do in the case where their paper doesn't get in?