From local averaging to emergent global behaviors: the fundamental role of network interconnections

Distributed averaging is one of the simplest and most studied network dynamics. Its applications range from cooperative inference in sensor networks, to robot formation, to opinion dynamics. A number of fundamental results and examples scattered through the literature are gathered here and originally presented, emphasizing the deep interplay between the network interconnection structure and the emergent global behavior.Comment: 10 page

Discrete Convex Functions on Graphs and Their Algorithmic Applications

The present article is an exposition of a theory of discrete convex functions on certain graph structures, developed by the author in recent years. This theory is a spin-off of discrete convex analysis by Murota, and is motivated by combinatorial dualities in multiflow problems and the complexity classification of facility location problems on graphs. We outline the theory and algorithmic applications in combinatorial optimization problems