  Motivated by practical concerns in the online advertising industry, we study
a bidder subset selection problem in single-item auctions. In this problem, a
large pool of candidate bidders have independent values sampled from known
prior distributions. The seller needs to pick a subset of bidders and run a
given auction format on the selected subset to maximize her expected revenue.
We propose two frameworks for the subset restrictions: (i) capacity constraint
on the set of selected bidders; and (ii) incurred costs for the bidders invited
to the auction. For the second-price auction with anonymous reserve (SPA-AR),
we give constant approximation polynomial time algorithms in both frameworks
(in the latter framework under mild assumptions about the market). Our results
are in stark contrast to the previous work of Mehta, Nadav, Psomas, Rubinstein
[NeurIPS 2020], who showed hardness of approximation for the SPA without a
reserve price. We also give complimentary approximation results for other
well-studied auction formats such as anonymous posted pricing and sequential
posted pricing. On a technical level, we find that the revenue of SPA-AR as a
set function $f(S)$ of its bidders $S$ is fractionally-subadditive but not
submodular. Our bidder selection problem with invitation costs is a natural
question about (approximately) answering a demand oracle for $f(\cdot)$ under a
given vector of costs, a common computational assumption in the literature on
combinatorial auctions.
