Frequency Capping in Online Advertising

We study the following online problem. Each advertiser ai has a value vi, demand di, and frequency cap fi. Supply units arrive online, each one associated with a user. Each advertiser can be assigned at most di units in all, and at most fi units from the same user. The goal is to design an online allocation algorithm maximizing total value. We first show a deterministic upper bound of 3/4-competitiveness, even when all frequency caps are 1, and all advertisers share identical values and demands. A competitive ratio approaching 1 - 1/e can be achieved via a reduction to a model with arbitrary decreasing valuations [GM07]. Our main contribution is analyzing two 3/4-competitive greedy algorithms for the cases of equal values, and arbitrary valuations with equal demands. Finally, we give a primal-dual algorithm which may serve as a good starting point for improving upon the 1 - 1/e ratio.