Machine learning has made remarkable progress, and a wide range of research has been conducted from theoretical and practical perspectives. However, the expansion of machine learning applications has raised novel concerns, such as data privacy and communication costs. This article outlines distributed machine learning methods such as federated learning (FL), which has been attracting attention in recent years as a method that can both fundamentally solve these problems and analyze big data. Then, we focus on decentralized FL (DFL), which does not have a centralized server. We describe the problems in wireless communication channels and countermeasures to solve them.

The class of simple-triangle graphs wasintroduced in the 1980s as a generalization of both interval graphs and permutation graphs. The recognition problem for simple-triangle graphs had been open, but in the early 2010s, a polynomial-time algorithm was proposed. This paper gives an overview of recent results on simple-triangle graphs with their related classes and then introduces some open questions.