Broadcast CONGEST Algorithms against Adversarial Edges

Abstract

We consider the corner-stone broadcast task with an adaptive adversary that controls a fixed number of t edges in the input communication graph. In this model, the adversary sees the entire communication in the network and the random coins of the nodes, while ma-liciously manipulating the messages sent through a set of t edges (unknown to the nodes). Since the influential work of [Pease, Shostak and Lamport, JACM’80], broadcast algorithms against plentiful adversarial models have been studied in both theory and practice for over more than four decades. Despite this extensive research, there is no round efficient broadcast algorithm for general graphs in the CONGEST model of distributed computing. Even for a single adversarial edge (i.e., t = 1), the state-of-the-art round complexity is polynomial in the number of nodes. We provide the first round-efficient broadcast algorithms against adaptive edge adver-saries. Our two key results for n -node graphs of diameter D are as follows: