So What is Complexity?

Many ways to study complexity, including
Classical Computational Complexity
Captures static properties
Upper/lower bounds on time, memory, etc of a given algorithm 
For example, a full mesh is said to have complexity O(n^2), since you need n*(n-1)/2 unique connections, and n*(n-1)/2 ~ c*n^2 = O(n^2) 
Many other techniques

In this talk we'll look at "Dynamical Systems Theory"
Focuses on a system's large scale, macroscopic properties 
That is, those *dynamic* properties that emerge at scale
Applies to the Internet as a system
Which is what we are interested in from an operational perspective
What kind of problems can we analyze this way?
The convergence behavior of BGP
BGP UPDATE propagation
The behavior of IGPs under congestion
PWE3 Alarm "multiplication"