Frequency capping in online advertising

Niv Buchbinder, Moran Feldman, Arpita Ghosh, Joseph Naor

Research output: Contribution to journalArticlepeer-review


We study the following online problem. There are n advertisers. Each advertiser ai has a total demand di and a value v i for each supply unit. Supply units arrive one by one in an online fashion, and must be allocated to an agent immediately. Each unit is associated with a user, and each advertiser ai is willing to accept no more than fi units associated with any single user (the value fi is called the frequency cap of advertiser ai). The goal is to design an online allocation algorithm maximizing the total value. We first show a deterministic 3/4 -competitiveness upper bound, which holds even when all frequency caps are 1, and all advertisers share identical values and demands. A competitive ratio approaching 1-1/e can be achieved via a reduction to a different model considered by Goel and Mehta (WINE '07: Workshop on Internet and Network, Economics: 335-340, 2007). Our main contribution is analyzing two 3/4 -competitive greedy algorithms for the cases of equal values, and arbitrary valuations with equal integral demand to frequency cap ratios. Finally, we give a primal-dual algorithm which may serve as a good starting point for improving upon the ratio of 1-1/e.

Original languageEnglish
Pages (from-to)385-398
Number of pages14
JournalJournal of Scheduling
Issue number4
StatePublished - Aug 2014
Externally publishedYes

Bibliographical note

Funding Information:
Acknowledgments We are extremely grateful to Ning Chen for several helpful discussions, and for first suggesting the total demand algorithm. Research supported in part by ISF Grant 954/11, and by BSF Grant 2010426. Research supported in part by the Google InterUniversity Center for Electronic Markets, by ISF Grant 954/11, and by BSF Grant 2010426.


  • Advertising
  • Competitive analysis
  • Frequency capping
  • Online allocation


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