Stochastic Input Models in Online Computing

TL;DR

This paper explores twelve stochastic input models in online algorithms, analyzing their relationships and impact on competitive ratios through applications to secretary and prophet inequality problems.

Contribution

It introduces a unified framework for twelve stochastic models, revealing their relationships and effects on online problem performance.

Findings

Different models yield varying competitive ratios.

Relationships among models help understand online problem complexities.

Applications to secretary and prophet problems illustrate model impacts.

Abstract

In this paper, we study twelve stochastic input models for online problems and reveal the relationships among the 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 model. To handle a broad class of online problems, we use a framework called request-answer games that is introduced by Ben-David et al. The stochastic input models consist of two types: known distribution and unknown distribution. For each type, we consider six classes of distributions: dependent distributions, deterministic input, independent distributions, identical independent distribution, random order of a deterministic input, and random order of independent distributions. As an application of the models, we consider two basic online problems, which are variants of the secretary problem and the prophet inequality problem, under the twelve stochastic input models. We see the difference of the competitive ratios through these problems.