## Abstract

We study the following online problem. There are n advertisers. Each advertiser a_{i} has a total demand d_{i} 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 a_{i} is willing to accept no more than f_{i} units associated with any single user (the value f_{i} is called the frequency cap of advertiser a_{i}). 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 language | English |
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Pages (from-to) | 385-398 |

Number of pages | 14 |

Journal | Journal of Scheduling |

Volume | 17 |

Issue number | 4 |

DOIs | |

State | Published - Aug 2014 |

Externally published | Yes |

### 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.

## Keywords

- Advertising
- Competitive analysis
- Frequency capping
- Online allocation