Limiting Behavior of Networks and nonstandard Analysis

Friday, March 2, 2001 - 10:10am - 11:00am
Vincent 570
Javier Thayer (The Mitre Corporation)
Computer scientists think of graphs primarily as discrete objects, which is fine when the number of nodes is small. However, as networks grow in size to the trillions of nodes, as they will with IPv6 in which virtually every electronic device will be networked, thinking about network topologies discretely, particularly in issues regarding security will be a disaster. In this talk we consider an alternative continuous view of newtorks

Specifically In this talk we will show the relation between discrete structures -- hyperfinite graphs-- and spaces which have nice growth properties. Such spaces can be very smooth but typically have fractal-like behavior. The unifying theme in this talk is an approach using nonstandard analysis. I will give a very brief vocabulary of nonstandard analysis at the beginning, so no special prerequisites are assumed.