An optimal algorithm for on-line bipartite matching
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
An optimal deterministic algorithm for online b-matching
Theoretical Computer Science
Online learning in online auctions
Theoretical Computer Science - Special issue: Online algorithms in memoriam, Steve Seiden
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Multi-unit auctions with unknown supply
EC '06 Proceedings of the 7th ACM conference on Electronic commerce
Improved Bounds for Online Routing and Packing Via a Primal-Dual Approach
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
A general approach to online network optimization problems
ACM Transactions on Algorithms (TALG)
Dynamic pricing for impatient bidders
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
AdWords and generalized online matching
Journal of the ACM (JACM)
A Primal-Dual Randomized Algorithm for Weighted Paging
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Randomized competitive algorithms for generalized caching
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Online Primal-Dual Algorithms for Covering and Packing
Mathematics of Operations Research
SIAM Journal on Computing
Online Ad Assignment with Free Disposal
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Online Stochastic Matching: Beating 1-1/e
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Online primal-dual algorithms for maximizing ad-auctions revenue
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Adwords auctions with decreasing valuation bids
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
Personalized ad delivery when ads fatigue: an approximation algorithm
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
New online algorithms for story scheduling in web advertising
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
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We study the following online problem. Each advertiser ai has a value vi, demand di, and frequency cap fi. Supply units arrive online, each one associated with a user. Each advertiser can be assigned at most di units in all, and at most fi units from the same user. The goal is to design an online allocation algorithm maximizing total value. We first show a deterministic upper bound of 3/4-competitiveness, 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 model with arbitrary decreasing valuations [GM07]. Our main contribution is analyzing two 3/4-competitive greedy algorithms for the cases of equal values, and arbitrary valuations with equal demands. Finally, we give a primal-dual algorithm which may serve as a good starting point for improving upon the 1 - 1/e ratio.