Broadly, I am interested in Network problems with current practical relevance but from which a fundamental concept can also be extracted, or to which one can be applied. Especially, I am interested in uncovering principles behind digital communication networks and use these principles to analyze, configure, and design protocols and services for the Internet.
In recent years, I have been deeply involved in Network Routing, as substantiated by the protocols of the Internet. The Internet routing system encompasses millions of destinations interconnected by millions of routers that work loosely together to deliver our messages. Although the number of routing protocols in use today is rather small, some of them, notably BGP, have a large configuration space, through which network operators strive to satisfy user expectations in a decentralized and competitive Internet.
My approach to routing is foundational, realizing that most routing protocols perform a distributed computation, which involves asynchronous iterations of two elemental operations: election of routes at a node and extension of routes from one node to a neighbor. This realization prompts a unifying, algebraic theory of routing. Within this theory, we can look for universal answers to questions posed by all routing protocols, such as:
· Under what conditions on the routing policies can we guarantee correct behavior of a routing protocol? Can these conditions be detected online?
· What can we say about the paths determined by a routing protocol? Are they optimal in some sense?
· To what extent do routing policies allow a complete use of the paths physically existing in a network? Is the resiliency of a network reduced by competitive routing policies?
· What are the space, message, and computational complexity induced by routing policies? Which routing policies lead to a scalable routing system?
As can be seen in publications of which I am a co-author, as well as in many other works, the algebraic theory of routing has been useful in establishing practical results in a variety of circumstances:
· Quality of service routing
· Wireless routing protocols
· Correct configuration of eBGP and of inter-domain routing
· Correct configuration of iBGP
· Security of BGP and of inter-domain routing
· Interconnection of different routing instances
· Scalability and inter-domain route aggregation
· Automatic design and verification of routing policies