Title: Birds of a Feather Flock Together Speaker: Yixin Cao, Polytechnic University Time/Date: Thursday, Feb 25, 11-12 am Location: Room 3494 Abstract: A simple observation in graphs is that some vertices are ``alike'': A set of vertices is a module if they have the same neighborhood outside this set, and they can be treated as a whole for many problems. A nice theory has been built on the properties of modules, and in particular, all the modules of a graph can be represented by a hierarchical tree structure. This provides a very handy, and sometimes indispensable, tool for solving a large family of graph problems. We survey the use of modules in algorithm design, including both classic results and our recent ones.