Chapter

Internet and Network Economics

Volume 5929 of the series Lecture Notes in Computer Science pp 374-385

Online Ad Assignment with Free Disposal

  • Jon FeldmanAffiliated withGoogle Inc.
  • , Nitish KorulaAffiliated withDept. of Computer Science, University of IllinoisWork done while at Google Inc., NY
  • , Vahab MirrokniAffiliated withGoogle Inc.
  • , S. MuthukrishnanAffiliated withGoogle Inc.
  • , Martin PálAffiliated withGoogle Inc.

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Abstract

We study an online weighted assignment problem with a set of fixed nodes corresponding to advertisers and online arrival of nodes corresponding to ad impressions. Advertiser a has a contract for n(a) impressions, and each impression has a set of weighted edges to advertisers. The problem is to assign the impressions online so that while each advertiser a gets n(a) impressions, the total weight of edges assigned is maximized.

Our insight is that ad impressions allow for free disposal, that is, advertisers are indifferent to, or prefer being assigned more than n(a) impressions without changing the contract terms. This means that the value of an assignment only includes the n(a) highest-weighted items assigned to each node a. With free disposal, we provide an algorithm for this problem that achieves a competitive ratio of 1 − 1/e against the offline optimum, and show that this is the best possible ratio. We use a primal/dual framework to derive our results, applying a novel exponentially-weighted dual update rule. Furthermore, our algorithm can be applied to a general set of assignment problems including the ad words problem as a special case, matching the previously known 1 − 1/e competitive ratio.