Motivated by the problem of optimizing allocation in guaranteed display advertising, we develop an efficient, lightweight method of generating a compact allocation plan that can be used to guide ad server decisions. The plan itself uses just O(1) state per guaranteed contract, is robust to noise, and allows us to serve (provably) nearly optimally.

A large fraction of online display advertising is sold via guaranteed contracts: a publisher guarantees to the advertiser a certain number of user visits satisfying the targeting predicates of the contract. The publisher is then tasked with solving the ad serving problem ---given a user visit, which of the thousands of matching contracts should be displayed, so that by the expiration time every contract has obtained the requisite number of user visits. The challenges of the problem come from (1) the sheer size of the problem being solved, with tens of thousands of contracts and billions of user visits, (2) the unpredictability of user behavior, since these contracts are sold months ahead of time, when only a forecast of user visits is available and (3) the minute amount of resources available online, as an ad server must respond with a matching contract in a fraction of a second.

We present a general framework and algorithmic approach for incremental approximation algorithms. The framework handles cardinality constrained minimization problems, such as the k-median and k-MST problems. Given some notion of ordering on solutions of different cardinalities k, we give solutions for all values of k such that the solutions respect the ordering and such that for any k, our solution is close in value to the value of an optimal solution of cardinality k. For instance, for the k-median problem, the notion of ordering is set inclusion, and our incremental algorithm produces solutions such that for any k and $k'$, $k

We consider the problem faced by a company that wants to use viral marketing to introduce a new product into a market where a competing product is already being introduced. We assume that consumers will use only one of the two products and will influence their friends in their decision of which product to use. We propose two models for the spread of influence of competing technologies through a social network and consider the influence maximization problem from the follower's perspective. In particular we assume the follower has a fixed budget available that can be used to target a subset of consumers and show that, although it is NP-hard to select the most influential subset to target, it is possible to give an efficient algorithm that is within 63% of optimal. Our computational experiments show that by using knowledge of the social network and the set of consumers targeted by the competitor, the follower may in fact capture a majority of the market by targeting a relatively small set of the right consumers.