Information Content of Online Problems. Advice versus Determinism and Randomization

In online computation, an algorithm has to solve some optimization problem while receiving the input instance gradually, without any knowledge about the future input. Such an online algorithm has to compute parts of the output for parts of the input, based on what it knows about the input so far and without being able to revoke its decisions later. Almost inevitably, the algorithm makes a bad choice at some point that leads to a solution that is suboptimal with respect to the whole input instance. Compared to an offline algorithm that is given the entire input instance at once, the online algorithm thus has a substantial handicap. Developing online algorithms that nonetheless compute solutions of some adequate quality is a large and rich field of research within computer science.