Online primal-dual algorithms for maximizing ad-auctions revenue

Abstract

We study the online ad-auctions problem introduced by Mehta et al. [15]. We design a (1-1/e)-competitive (optimal) algorithm for the problem, which is based on a clean primal-dual approach, matching the competitive factor obtained in [15]. Our basic algorithm along with its analysis are very simple. Our results are based on a unified approach developed earlier for the design of online algorithms [7,8]. In particular, the analysis uses weak duality rather than a tailor made (i.e., problem specific) potential function. We show that this approach is useful for analyzing other classical online algorithms such as ski rental and the TCP-acknowledgement problem. We are confident that the primal-dual method will prove useful in other online scenarios as well. The primal-dual approach enables us to extend our basic ad-auctions algorithm in a straight forward manner to scenarios in which additional information is available, yielding improved worst case competitive factors. In particular, a scenario in which additional stochastic information is available to the algorithm, a scenario in which the number of interested buyers in each product is bounded by some small number d, and a general risk management framework. © Springer-Verlag Berlin Heidelberg 2007.