Abstract

Many search engines auction the advertising space alongside search results. When Google inter-viewed Amin Saberi in 2004, their advertisement model became the focus of a new research area. Although he did not land the job, the interview was an important stimulus in his academic ca-reer. Upon his return to Georgia Tech, Saberi shared the question with another graduate student, Aranyak Mehta, and their thesis advisor, Vijay Vazirani. Vazirani recognized a connection between this new problem and the online bipartite matching problem, a problem he had solved 14 years earllier. When the Vazirani brothers and Karp proved a solution to it in 1990, the researchers saw online matching as a beautiful research problem. Umesh Vazirani says. “At the time, we had no idea it would turn out to have practical value. ” [7] Based on previous algorithms for online allocation, Mehta et. al. devised an innovative deterministic algorithm. They prove the optimality of their algorithm in the general case when there is no prior knowledge about the input queries. The primary assumption of the algorithm is that bids are small compared to an advertiser’s daily budget. [5] Together with Gagan Goel, Mehta explored the Adwords problem when assumptions can be made about the distribution of search queries. They showed that a simple greedy algorithm achieves the