Towards an Algebra of Routing Tables
We use well-known algebraic concepts like semirings and matrices to model and argue about Wireless Mesh Networks. These networks are used in a wide range of application areas, including public safety and transportation. Formal reasoning therefore seems to be necessary to guarantee safety and security. In this paper, we model a simplified algebraic version of the AODV protocol and provide some basic properties. For example we show that each node knows a route to the originator of a message (if there is one).
KeywordsControl Message Wireless Mesh Network Route Request Route Reply Route Table
Unable to display preview. Download preview PDF.
- 1.AODV-UU: An implementation of the AODV routing protocol (IETF RFC 3561), http://sourceforge.net/projects/aodvuu/ (accessed February 26, 2011)
- 2.Backhouse, R.: Closure Algorithms and the Star-Height Problem of Regular Languages. Ph.D. thesis, Imperial College, London (1975)Google Scholar
- 3.Backhouse, R., Carré, B.A.: Regular algebra applied to path-finding problems. Journal of the Institute of Mathematics and Applications (1975)Google Scholar
- 12.Höfner, P.: Database for automated proofs of Kleene algebra, http://www.kleenealgebra.de (accessed February 26, 2011)
- 16.McCune, W.W.: Prover9 and Mace4, http://www.cs.unm.edu/~mccune/prover9 (accessed February 26, 2011)
- 18.Möller, B.: Dijkstra, Kleene, Knuth. Talk at WG2.1 Meeting, slides available online, at http://web.comlab.ox.ac.uk/jeremy.gibbons/wg21/meeting61/MoellerDijkstra.pdf (accessed February 26, 2006)
- 20.Perkins, C., Belding-Royer, E., Das, S.: Ad hoc on-demand distance vector (AODV) routing. RFC 3561 (Experimental) (July 2003), http://www.ietf.org/rfc/rfc3561.txt
- 23.Sobrinho, J.: Network routing with path vector protocols: Theory and applications. In: Applications, Technologies, Architectures, and Protocols for Computer Communications. SIGCOMM 2003, pp. 49–60. ACM Press, New York (2003)Google Scholar
- 24.Takai, T., Furusawa, H.: Monodic tree kleene algebra. In: Schmidt, R.A. (ed.) RelMiCS/AKA 2006. LNCS, vol. 4136, pp. 402–416. Springer, Heidelberg (2006) (accessed February 26, 2011) Errata available at http://www.sci.kagoshima-u.ac.jp/~furusawa/person/Papers/correct_ monodic_kleene_algebra.pdf Google Scholar