Should I agree to review a paper that I do not fully understand? I recently received a request to subreview a paper for a top computer science conference. While it is related to my field of research, it is extremely long (the conference does not have a page limit) and complicated (it is an algorithm made of more than ten sub-algorithms, each of which is itself worth a conference paper). I find it very difficult to verify that it is correct. I mean, theoretically I may be able to understand it if I spend several whole weeks on reading every sub-algorithm, crafting small examples to myself, writing comupter simulations etc., but then I will have to stop doing anything else. What should I do?


Decline the request, hoping that the paper will be given to a smarter reviewer that will be more capable of verifying its correctness? Or -
Agree to the request, but tell the PC member in advance that I am going to review only a part of the paper which I can understand?


NOTE: The problem is not with the authors' presentation. In fact, their explanations seem good and clear. Just the algorithms themselves are highly complex.
I would go with 2, or at least contact the editor saying you would do 2, and asking if they'd prefer 1. There tends to be a shortage of referees, at least in my field, so I'd expect 2 to be preferred. I've been sent a paper to look at one aspect where someone else had apparently already checked a different aspect.

While I hate to say it, I believe in maths it would not really be expected that every tiny detail of a similar paper would be checked. I used to think it worked like that, but the time issues you mention are true for others too, so I guess 'certain enough' has to replace 'absolutely certain'.