The Internet routing system is composed of millions of routers running one or more of several routing protocols---BGP, OPSF, IS-IS, RIP, EIGRP, DSR, AODV, OLSR, RPL---with the goal of guiding data-packets from sources to destinations. Beyond the specificity of every routing protocol, a number of questions are pertinent across wide classes of them, namely:
- Does the routing protocol always terminate in a stable state devoid of forwarding loops and forwarding deflections?
- Are the paths followed by data-packets optimal in some sense?
- How much of the inherent resiliency of the network does the routing protocol exploit?
- Does the routing protocol scale with the number of destinations?
Routing selects paths for the transport of data-packets indirectly, through attributes they possess. Routing protocols operate by continually interleaving two processes: that of computing attributes of paths from characteristics of its constituent links; and that of choosing best attributes. The algebraic approach studies how the entwining of these two processes determines the global behavior of a routing protocol, providing answers to the questions above.
In this talk, I will illustrate the unifying power of the algebraic approach by delving into the non-optimality of paths determined by EIGRP (Enhanced Interior Gateway Routing Protocol) and termination and resiliency issues raised by BGP (Border Gateway Protocol). In addition, I will survey recent applications of the algebraic approach, notably to the interconnection of routing instances and to route aggregation in the Internet.
João Luís Sobrinho received his Licenciatura and Ph.D. degrees in Electrical and Computer Engineering from the Technical University of Lisbon, Portugal, in 1990 and 1995, respectively. During 1995 and 1996, he was a Member of the Technical Staff at Bell Labs, Nieuwegein, The Netherlands; he further consulted for Bell Labs, Murray Hill, NJ, from 1997 to 1999. He is currently Associate Professor at the Faculty of Engineering of the Technical University of Lisbon and a Researcher at the Telecommunications Institute. Prof. Sobrinho is a member of the IEEE and of the ACM.