Near optimal online algorithms and fast approximation algorithms for resource allocation problems

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.