Combinatorial Problems in Online Advertising
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Electronic commerce or eCommerce refers to the process of buying and selling of goods and services over the Internet. In fact, the Internet has completely transformed traditional media based advertising so much so that billions of dollars of advertising revenue is now flowing to search companies such as Microsoft, Yahoo! and Google. In addition, the new advertising landscape has opened up the advertising industry to all players, big and small. However, this transformation has led to a host of new problems faced by the search companies as they make decisions about how much to charge for advertisements, whose ads to display to users, and how to maximize their revenue. In this thesis we focus on an entire suite of problems motivated by the central question of "Which advertisement to display to which user?". Targeted advertisement happens when a user enters a relevant search query. The ads are usually displayed on the sides of the search result page. Internet advertising also takes place by displaying ads on the side of webpages with relevant content. While large advertisers (e.g. Coca Cola) pursue brand recognition by advertisement, small advertisers are happy with instant revenue as a result of a user following their ad and performing a desired action (e.g. making a purchase). Therefore, small advertisers are often happy to get any ad slot related to their ad while large advertisers prefer contracts that will guarantee that their ads will be delivered to enough number of desired users. We first focus on two problems that come up in the context of small advertisers. The first problem we consider deals with the allocation of ads to slots considering the fact that users enter search queries over a period of time, and as a result the slots become available gradually. We use a greedy method for allocation and show that the online ad allocation problem with a fixed distribution of queries over time can be modeled as maximizing a continuous non-decreasing submodular sequence function for which we can guarantee a solution with a factor of at least (1- 1/e) of the optimal. The second problem we consider is query rewriting problem in the context of keyword advertisement. This problem can be posed as a family of graph covering problems to maximize profit. We obtain constant-factor approximation algorithms for these covering problems under two sets of constraints and a realistic notion of ad benefit. We perform experiments on real data and show that our algorithms are capable of outperforming a competitive baseline algorithm in terms of the benefit due to rewrites. We next consider two problems related to premium customers, who need guaranteed delivery of a large number of ads for the purpose of brand recognition and would require signing a contract. In this context, we consider the allocation problem with the objective of maximizing either revenue or fairness. The problems considered in this thesis address just a few of the current challenges in e-Commerce and Internet Advertising. There are many interesting new problems arising in this field as the technology evolves and online-connectivity through interactive media and the internet become ubiquitous. We believe that this is one of the areas that will continue to receive greater attention by researchers in the near future.