Dynamic algorithm for determining a shortest path tree between network nodes

Abstract

A dynamic shortest path tree (SPT) algorithm for a router determines a new SPT for a root node in response to a link-state or other network topology change. The dynamic SPT algorithm determines the new SPT as an optimization problem in a linear programming framework based in an existing SPT in the router. The dynamic SPT algorithm emulates maximum decrement of a ball and string model by iteratively selecting nodes of the existing SPT for consideration and update of parent node, child nodes, and distance attributes based on the maximum decrement. For the maximum decrement, a node in the existing SPT is selected by each iteration based on the greatest potential decrease (or least increase) in its distance attribute. The ball and string model that may be employed for the dynamic SPT algorithm represents a network of nodes and links with a ball representing a node and a string representing a link or edge. The length of a string is defined by its link's weight. The set of strings connecting the balls defines a path between the root node and a particular node. The shortest path is the path defined by the strings from a root node to a particular node that are tight. For the dynamic SPT algorithm, an increase (or decrease) in an edge weight in an existing SPT corresponds to a lengthening (or shortening) of a string. By sequentially pulling balls away in a single direction from the ball of the root node, the new SPT becomes defined by the balls and tight strings.