Global Uniform Asymptotic Stability of a Generalized Adaptive Bellman-Ford Algorithm

Abstract

Self-stabilizing information spreading algorithms are a key basis block for building distributed system for device coordination. The adaptive Bellman-Ford (ABF) algorithm is a special case of these spreading algorithms. It finds the distance estimate of each node in a graph from a source set, but unlike the classical Bellman-Ford algorithm does not assume that all initial distance estimates exceed their true values. Though globally uniformly asymptotically stable (GUAS), its convergence can be very slow in graphs will short edges if some initial estimates are smaller than their true values. We propose here a generalization of ABF with additional parameters to permit faster convergence. We prove it to be GUAS, bounding the time to converge, and show via simulations that it withstands persistent bounded perturbations in the graph edge lengths.