Dr. Tim Griffin: An Algebraic Approach to Internet Routing

Seminar: An Algebraic Approach to Internet Routing
Instructor: Prof. Dr. Tim Griffin, University of Cambridge
Location: Room 4.1F03, Telematics Department, Torres Quevedo Building, University Carlos III of Madrid, Avda. Universidad, 30, 28911 Leganes – Madrid
Dates: 16th –18th March, 2009
16th & 17th March: 10:00 – 13:30
18th: 10:00 – 13:00
Organization: NETCOM Research Group (Telematics Department, University Carlos III of Madrid, Spain); IMDEA Networks (Madrid, Spain)

The seminar will be conducted in English

Abstract:

An Algebraic Approach to Internet Routing

Agreat deal of of interesting work was done in the 1970s in generalizingshortest path algorithms to a wide class of semirings also called «pathalgebras» or «dioids». Although the evolution of Internet Routingprotocols does not seem to have taken much inspiration from this work,recent «reverse engineering» efforts have demonstrated that analgebraic approach is very useful for both understanding existingprotocols and for exploring the design space of future Internet routingprotocols. This course is intended teach participants the basicconcepts needed to understand this approach. No previous backgroundwill be assumed. The course will start from scratch and end with openresearch problems. Many examples inspired by Internet Routing will bepresented along the way. The Metarouting Toolkit,currently beingdeveloped at Cambridge, will be introduced. This tool allows users togenerate a routing protocols implementation (in C code) from adeclarative, high-level specification based on the algebraic modelspresented in this course.

Outline of Lectures:
1. What is right and wrong with Internet Routing?
2. An overview of algebraic routing
3. Semigroups and orders
4. Semirings
5. Solving Path Problems in Graphs with semirings
6. What is the difference between routing and forwarding tables?
7. Modeling Interior Gateway Protocols (IGPs)
8. Modeling BGP-like routing
9. Constructing Routing Algebras for Internet Routing
10. Metarouting

Recommended (but not required) reading:
1. Graphs, Dioids, and Semirings : New Models and Algorithms. M. Gondran and M. Minoux. Springer 2008.
2. Regular Algebra Applied to Path-Finding Problems. R.C. Backhouse and B.A.Carr J.Inst.Maths.Applics (1975) 15, 161=96186.
3.J. L. Sobrinho, «Algebra and Algorithms for QoS Path Computation andHop-by-Hop Routing in the Internet,» IEEE/ACM Transactions onNetworking, pp. 541-550, August 2002.
4. J. L. Sobrinho, «NetworkRouting With Path Vector Protocols: Theory and Applications» in Proc.ACM SIGCOMM 2003, pp. 49-60, Karlsruhe, Germany, August 2003.
5. J. L. Sobrinho, «An Algebraic Theory of Dynamic Network Routing,»
IEEE/ACM Transactions on Networking, pp. 1160-1173, October 2005.
6. Metarouting. Timothy G. Griffin and Joo Lus Sobrinho. SIGCOMM 2005.
7. Lexicographic Products in Metarouting. Alexander Gurney, Timothy
G. Griffin. ICNP, October 2007, Beijing.
8. Increasing Bisemigroups and Algebraic Routing. Timothy G. Griffin and Alexander Gurney, RelMiCS10, April 2008.