STOCHASTIC INPUT MODELS FOR ONLINE COMPUTING

In this paper, we study twelve stochastic input models for online problems and reveal the differences between their competitive ratios for the models. The competitive ratio is defined as the worst ratio between the expected optimal value and the expected profit of the solution obtained by the online algorithm, where the input distribution is restricted according to the input model. Our purpose is to clarify the difference among the input models from the view of the competitive ratio. To handle a broad class of online problems, we use a framework called request-answer games, which were introduced by Ben-David et al. The stochastic input models fit into two categories: known distribution and unknown distribution. We consider six natural classes of distribution for each category: dependent distributions, deterministic input, independent distributions, identical independent distribution, random order of a deterministic input, and random order of independent distributions. Using each input model, we consider two fundamental online problems, which are variants of the secretary problem and the prophet inequality problem. We use these problems to observe the difference in the competitive ratios of each input model.