New dynamic algorithms for shortest path tree computation

TLDR: An algorithmic framework is established that allows for 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.

Abstract: 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