New dynamic algorithms for shortest path tree computation

The open shortest path first (OSPF) and IS-IS routing protocols widely used in today's Internet compute a shortest path tree (SPT) from each router to other routers in a routing area. Many existing commercial routers recompute an SPT from scratch following changes in the link states of the network. Such recomputation of an entire SPT is inefficient and may consume a considerable amount of CPU time. Moreover, as there may coexist multiple SPTs in a network with a set of given link states, recomputation from scratch causes frequent unnecessary changes in the topology of an existing SPT and may lead to routing instability. We present new dynamic SPT algorithms that make use of the structure of the previously computed SPT. Besides efficiency, our algorithm design objective is to achieve routing stability by making minimum changes to the topology of an existing SPT (while maintaining shortest path property) when some link states in the network have changed. We establish an algorithmic framework that allows us to characterize a variety of dynamic SPT algorithms including dynamic versions of the well-known Dijkstra, Bellman-Ford, D'Esopo-Pape algorithms, and to establish proofs of correctness for these algorithms in a unified way. The theoretical asymptotic complexity of our new dynamic algorithms matches the best known results in the literature.

[1]  Alberto Marchetti-Spaccamela,et al.  Dynamic algorithms for shortest paths in planar graphs , 1993, Theor. Comput. Sci..

[2]  Daniele Frigioni,et al.  Incremental algorithms for single-source shortest path trees , 1994 .

[3]  Christian Huitema,et al.  Routing in the Internet , 1995 .

[4]  John Moy,et al.  OSPF Version 2 , 1998, RFC.

[5]  Daniele Frigioni,et al.  Incremental Algorithms for the Single-Source Shortest Path Problem , 1994, FSTTCS.

[6]  J. J. Garcia-Luna-Aceves,et al.  A path-finding algorithm for loop-free routing , 1997, TNET.

[7]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[8]  Thomas W. Reps,et al.  An Incremental Algorithm for a Generalization of the Shortest-Path Problem , 1996, J. Algorithms.

[9]  Richard Bellman,et al.  ON A ROUTING PROBLEM , 1958 .

[10]  M. Steenstrup.  Routing in communications networks , 1995 .

[11]  R. Tarjan.  Amortized Computational Complexity , 1985 .

[12]  Pawel Gburzynski,et al.  Routing in multihop packet switching networks: Gb/s challenge , 1995, IEEE Netw..

[13]  M. Schwartz,et al.  Routing Techniques Used in Computer Communication Networks , 1980, IEEE Trans. Commun..

[14]  Christian Huitema,et al.  An Architecture for Residential Internet Telephony Service , 1999, IEEE Internet Comput..

[15]  G. Varghese,et al.  Pitfalls in the design of distributed routing algorithms , 1988, SIGCOMM 1988.

[16]  Dave Katz,et al.  Application of the Border Gateway Protocol in the Internet , 1990, RFC.

[17]  Eric C. Rosen,et al.  The New Routing Algorithm for the ARPANET , 1980, IEEE Trans. Commun..

[18]  Daniele Frigioni,et al.  Fully dynamic output bounded single source shortest path problem , 1996, SODA '96.

[19]  Stephen E. Deering,et al.  Multicast routing in datagram internetworks and extended LANs , 1990, TOCS.

[20]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

[21]  Giuseppe F. Italiano,et al.  Incremental algorithms for minimal length paths , 1991, SODA '90.

[22]  R. Perlman.  A comparison between two routing protocols: OSPF and IS-IS , 1991, IEEE Network.

[23]  A. Pan,et al.  On Finding and Updating Spanning Trees and Shortest Paths , 1975, SIAM J. Comput..

[24]  J. Moy,et al.  OSPF: Anatomy of an Internet Routing Protocol , 1998 .

[25]  Daniele Frigioni,et al.  Semi-Dynamic Shortest Paths and Breadth-First Search in Digraphs , 1997, STACS.

[26]  Deborah Estrin,et al.  Design of inter-administrative domain routing protocols , 1990, SIGCOMM 1990.

[27]  Vern Paxson,et al.  End-to-end routing behavior in the Internet , 1996, TNET.

[28]  Farnam Jahanian,et al.  Internet routing instability , 1997, SIGCOMM '97.

[29]  Dimitri P. Bertsekas,et al.  Linear network optimization - algorithms and codes , 1991 .