Discrete configurations and combinatorial methods originated from distributed network

Abstract

In recent years, many new problems of information science originating from distributed networks have brought new challenges to the classical information theory and coding theory. The research of these problems involves many discrete configurations. Combinatorial methods such as combinatorial design theory, graph theory, combinatorial coding theory and extremal combinatorics have been playing an important role in the research of these problems. In this paper, we briefly survey the progress on five hot frontier topics originating from distributed networks, including network coding, index coding, coded caching, distributed computing, and private information retrieval. In particular, we emphasize the discrete configurations and combinatorial methods related to these topics. For some of the topics, we also provide a few new results.