New dynamic SPT algorithm based on a ball-and-string model

Abstract

A key functionality in today's widely used interior gateway routing protocols such as OSPF and IS-IS involves the computation of a shortest path tree (SPT). In many existing commercial routers, the computation of an SPT is done from scratch following changes in the link states of the network. As there may coexist multiple SPTs in a network with a set of given link states, such recomputation of an entire SPT not only is inefficient but also causes frequent unnecessary changes in the topology of an existing SPT and creates routing instability. This paper presents a new dynamic SPT algorithm that makes use of the structure of the previously computed SPT. Our algorithm is derived by recasting the SPT problem into an optimization problem in a dual linear programming framework, which can also be interpreted using a ball-and-string model. In this model, the increase (or decrease) of an edge weight in the tree corresponds to the lengthening (or shortening) of a string. By stretching the strings until each node is attached to a tight string, the resulting topology of the model defines an (or multiple) SPT(s). By emulating the dynamics of the ball-and-string model, we can derive an efficient algorithm that propagates changes in distances to all affected nodes in a natural order and in a most economical way. Compared with existing results, our algorithm has the best-known performance in terms of computational complexity as well as minimum changes made to the topology of an SPT. Rigorous proofs for correctness of our algorithm and simulation results illustrating its complexity are also presented.