An optimal algorithm for on-line bipartite matching
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Journal of Algorithms
AdWords and generalized online matching
Journal of the ACM (JACM)
Online budgeted matching in random input models with applications to Adwords
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
On-line bipartite matching made simple
ACM SIGACT News
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
Tight thresholds for cuckoo hashing via XORSAT
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Improved bounds for online stochastic matching
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
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
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We consider the online stochastic matching problem proposed by Feldman et al. [Feldman J, Mehta A, Mirrokni VS, Muthukrishnan S (2009) Online stochastic matching: Beating 1-1/e. Annual IEEE Sympos. Foundations Comput. Sci. 117--126] as a model of display ad allocation. We are given a bipartite graph; one side of the graph corresponds to a fixed set of bins, and the other side represents the set of possible ball types. At each time step, a ball is sampled independently from the given distribution and it needs to be matched upon its arrival to an empty bin. The goal is to maximize the number of allocations. We present an online algorithm for this problem with a competitive ratio of 0.702. Before our result, algorithms with a competitive ratio better than 1-1/e were known under the assumption that the expected number of arriving balls of each type is integral. A key idea of the algorithm is to collect statistics about the decisions of the optimum offline solution using Monte Carlo sampling and use those statistics to guide the decisions of the online algorithm. We also show that our algorithm achieves a competitive ratio of 0.705 when the rates are integral. On the hardness side, we prove that no online algorithm can have a competitive ratio better than 0.823 under the known distribution model (and henceforth under the permutation model). This improves upon the 5/6 hardness result proved by Goel and Mehta [Goel G, Mehta A (2008) Online budgeted matching in random input models with applications to adwords. ACM-SIAM Symposium Discrete Algorithms 982--991] for the permutation model.