On-line Network Optimization Problems
Developments from a June 1996 seminar on Online algorithms: the state of the art
AdWords and Generalized On-line Matching
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
The adwords problem: online keyword matching with budgeted bidders under random permutations
Proceedings of the 10th ACM conference on Electronic commerce
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
Fast algorithms for finding matchings in lopsided bipartite graphs with applications to display ads
Proceedings of the 11th ACM conference on Electronic commerce
Improved bounds for online stochastic matching
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Near optimal online algorithms and fast approximation algorithms for resource allocation problems
Proceedings of the 12th ACM conference on Electronic commerce
Online bipartite matching with unknown distributions
Proceedings of the forty-third annual ACM symposium on Theory of computing
Online bipartite matching with random arrivals: an approach based on strongly factor-revealing LPs
Proceedings of the forty-third annual ACM symposium on Theory of computing
Simultaneous approximations for adversarial and stochastic online budgeted allocation
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Mechanism design via correlation gap
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Online stochastic matching: online actions based on offline statistics
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Online stochastic weighted matching: improved approximation algorithms
WINE'11 Proceedings of the 7th international conference on Internet and Network Economics
Budget smoothing for internet ad auctions: a game theoretic approach
Proceedings of the fourteenth ACM conference on Electronic commerce
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In this paper we consider the adwords problem in the unknown distribution model. We consider the case where the budget to bid ratio k is at least 2, and give improved competitive ratios. Earlier results had competitive ratios better than 1-1/e only for "large enough" k, while our competitive ratio increases continuously with k. For k=2 the competitive ratio we get is 0.729 and it is 0.9 for k=16. We also improve the asymptotic competitive ratio for large k from 1 - O(√log n/k) to 1 - O(√1/k), thus removing any dependence on n, the number of advertisers. This ratio is optimal, even with known distributions. That is, even if an algorithm is tailored to the distribution, it cannot get a competitive ratio of 1 - o(√1/k), whereas our algorithm does not depend on the distribution. The algorithm is rather simple, it computes a score for every advertiser based on his original budget, the remaining budget and the remaining number of steps in the algorithm and assigns a query to the advertiser with the highest bid plus his score. The analysis is based on a "hybrid argument" that considers algorithms that are part actual, part hypothetical, to prove that our (actual) algorithm is better than a completely hypothetical algorithm whose performance is easy to analyze.