Matching Auctions for Search and Native Ads.

Unit demand auctions power today's search and native ad marketplaces. Traditional implementations make an extreme "separability" assumption: the relative value of any two ad slots is the same for all advertisers. Under this assumption, the optimal assignment problem can be conveniently solved simply by sorting; without it, efficient allocation requires solving a full-blown weighted matching problem. Motivated by prior work and our own empirical evidence against separability, we abandon that assumption and tackle the algorithmic problems of assignment and pricing for general unit demand ad auctions. Instead of computing prices directly, we take a novel approach and compute bidders' full allocation curves---complete mappings from each agent's bid space to their allocation under the optimal assignment function---from which it is trivial to compute most prices of interest, like those of the Generalized Second Price (GSP) or Vickrey-Clarke-Groves (VCG) auctions. Remarkably, we show that these full allocation curves (and therefore prices) can be computed in the same asymptotic runtime required to compute the optimal matching alone.