Advice complexity: Quantitative approach to a-priori information (extended abstract)

Abstract

We survey recent results from different areas, studying how introducing per-instance a-priori information affects the solvability and complexity of given tasks. We mainly focus on distributed, and online computation, where some sort of hidden information plays a crucial role: in the distributed computing, typically nodes have no or only limited information about the global state of the network; in online problems, the algorithm lacks the information about the future input. The traditional approach in both areas is to study how the properties of the problem change if some partial information is available (e.g., nodes of a distributed system have sense of direction, the online algorithm has the promise that the input requests come in some specified order etc.). Recently, attempts have been made to study this information from a quantitative point of view: there is an oracle that delivers (per-instance) best-case information of a limited size, and the relationship between the amount of the additional information, and the benefit it can provide to the algorithm, is investigated. We show cases where this relationship has a form of a trade-off, and others where one or more thresholds can be identified. © 2014 Springer International Publishing Switzerland.