An optimal algorithm for on-line bipartite matching
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Randomized algorithms
An optimal deterministic algorithm for online b-matching
Theoretical Computer Science
AdWords and Generalized On-line Matching
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Online budgeted matching in random input models with applications to Adwords
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Improved Approximation Algorithms for Budgeted Allocations
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Budgeted Allocations in the Full-Information Setting
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
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
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
Online algorithms with stochastic input
ACM SIGecom Exchanges
Simultaneous approximations for adversarial and stochastic online budgeted allocation
Proceedings of the twenty-third 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
Online matching with concave returns
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Asymptotically optimal algorithm for stochastic adwords
Proceedings of the 13th ACM Conference on Electronic Commerce
Online Stochastic Matching: Online Actions Based on Offline Statistics
Mathematics of Operations Research
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We study the online stochastic matching problem in a form motivated by Internet display advertisement. Recently, Feldman et al. gave an algorithm that achieves 0.6702 competitive ratio, thus breaking through the 1-1/e barrier. One of the questions left open in their work is to obtain a better competitive ratio by generalizing their two suggested matchings (TSM) algorithm to d-suggested matchings (d-SM). We show that the best competitive ratio that can be obtained with the static analysis used in the d-SM algorithm is upper bounded by 0.76, even for the special case of d-regular graphs, thus suggesting that a dynamic analysis may be needed to improve the competitive ratio significantly. We make the first step in this direction by showing that the RANDOM algorithm, which assigns an impression to a randomly chosen eligible advertiser, achieves 1 - e-ddd/d! = 1-O(1/√d) competitive ratio for d-regular graphs, which converges to 1 as d increases. On the hardness side, we improve the upper bound of 0.989 on the competitive ratio of any online algorithm obtained by Feldman et al. to 1-1/(e + e2) ≅ 0.902. Finally, we show how to modify the TSM algorithm to obtain an improved 0.699 approximation for general bipartite graphs.