Online Ad Assignment with Free Disposal

  • Authors:
  • Jon Feldman;Nitish Korula;Vahab Mirrokni;S. Muthukrishnan;Martin Pál

  • Affiliations:
  • Google Inc., New York 10011;Dept. of Computer Science, University of Illinois, Urbana 61801 and Work done while at Google Inc., NY,;Google Inc., New York 10011;Google Inc., New York 10011;Google Inc., New York 10011

  • Venue:
  • WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
  • Year:
  • 2009

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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 驴 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 驴 1/e competitive ratio.