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Randomized rounding without solving the linear program
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Routing and admission control in general topology networks with Poisson arrivals
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An optimal deterministic algorithm for online b-matching
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Approximating Fractional Multicommodity Flow Independent of the Number of Commodities
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AdWords and Generalized On-line Matching
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Online budgeted matching in random input models with applications to Adwords
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The adwords problem: online keyword matching with budgeted bidders under random permutations
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Online Stochastic Matching: Beating 1-1/e
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Online primal-dual algorithms for maximizing ad-auctions revenue
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Fast algorithms for finding matchings in lopsided bipartite graphs with applications to display ads
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Improved bounds for online stochastic matching
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Online stochastic packing applied to display ad allocation
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Online stochastic matching: online actions based on offline statistics
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Fractional matching via balls-and-bins
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Online algorithms with stochastic input
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Simultaneous approximations for adversarial and stochastic online budgeted allocation
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Online selection of diverse results
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Online stochastic weighted matching: improved approximation algorithms
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Online matching with concave returns
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Online prophet-inequality matching with applications to ad allocation
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Asymptotically optimal algorithm for stochastic adwords
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Geometry of online packing linear programs
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Whole-page optimization and submodular welfare maximization with online bidders
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We present algorithms for a class of resource allocation problems both in the online setting with stochastic input and in the offline setting. This class of problems contains many interesting special cases such as the Adwords problem. In the online setting we introduce a new distributional model called the adversarial stochastic input model, which is a generalization of the i.i.d model with unknown distributions, where the distributions can change over time. In this model we give a 1-O(ε) approximation algorithm for the resource allocation problem, with almost the weakest possible assumption: the ratio of the maximum amount of resource consumed by any single request to the total capacity of the resource, and the ratio of the profit contributed by any single request to the optimal profit is at most (ε2/log(1/ε)2)/(log n + log (1/ε)) where n is the number of resources available. There are instances where this ratio is #949;2/log n such that no randomized algorithm can have a competitive ratio of 1-o(ε) even in the i.i.d model. The upper bound on ratio that we require improves on the previous upper-bound for the i.i.d case by a factor of n. Our proof technique also gives a very simple proof that the greedy algorithm has a competitive ratio of 1-1/e for the Adwords problem in the i.i.d model with unknown distributions, and more generally in the adversarial stochastic input model, when there is no bound on the bid to budget ratio. All the previous proofs assume that either bids are very small compared to budgets or something very similar to this. In the offline setting we give a fast algorithm to solve very large LPs with both packing and covering constraints. We give algorithms to approximately solve (within a factor of 1+ε) the mixed packing-covering problem with O(γ m log n/ε2) oracle calls where the constraint matrix of this LP has dimension n x m, and γ is a parameter which is very similar to the ratio described for the online setting. We discuss several applications, and how our algorithms improve existing results in some of these applications.