Should I agree to review a paper that I do not fully understand?

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Question

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?

  1. Decline the request, hoping that the paper will be given to a smarter reviewer that will be more capable of verifying its correctness? Or -

  2. 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.

Answer

As an editor of a journal, I'd encourage you to contact the editor stating pretty much what you've said here and offer to review the paper as best you can in light of those limitations, should they want that.

This is for two reasons.

  1. The editor is probably less of an expert in this than you are. Editors see all sorts of papers spanning dozens of subfields and do their best to find folks who have a reasonable chance of understanding what the paper's about and whether it's interesting. That you've been asked to review the paper means, somewhere, an editor thinks that you have a special knowledge of this particular subtopic.

  2. There is probably a lot you can do here, even if you don't have the time or ability to follow all of the authors' arguments. Does the argument appear well-crafted? Do the ideas fit together? Does the paper seem as though it will be of interest to people? Refer back to Point 1: from the Editor's perspective the paper may be jargony, rely on methods that are more obscure to them than to you, and may be of dubious interest. Your opinions may matter.