Who Should Google Scholar Update More Often?

We consider a resource-constrained updater, such as Google Scholar, which wishes to update the citation records of a group of researchers, who have different mean citation rates (and optionally, different importance coefficients), in such a way to keep the overall citation index as up to date as possible. The updater is resource-constrained and cannot update citations of all researchers all the time. In particular, it is subject to a total update rate constraint that it needs to distribute among individual researchers. We use a metric similar to the age of information: the long-term average difference between the actual citation numbers and the citation numbers according to the latest updates. We show that, in order to minimize this difference metric, the updater should allocate its total update capacity to researchers proportional to the square roots of their mean citation rates. That is, more prolific researchers should be updated more often, but there are diminishing returns due to the concavity of the square root function. More generally, our paper addresses the problem of optimal operation of a resource-constrained sampler that wishes to track multiple independent counting processes in a way that is as up to date as possible.