A Simple and General Problem and its Optimal Randomized Online Algorithm Design with Competitive Analysis

The online algorithm design was proposed to handle the caching problem when the future information is unknown. And currently, it draws more and more attentions from the researchers from the areas of microgrid, where the production of renewables are unpredictable. In this note, we present a framework of randomized online algorithm design for the \textit{simple and tractable} problem. This framework hopes to provide a tractable design to design a randomized online algorithm, which can be proved to achieve the best competitive ratio by \textit{Yao's Principle}.