Distributed Computations in Fully-Defective Networks

TL;DR

This paper demonstrates that reliable distributed computation is possible in fully-defective asynchronous networks that are 2-edge connected by constructing special cycles, despite all messages potentially being corrupted.

Contribution

It introduces a method to simulate noiseless algorithms in fully-defective networks using Robbins cycles, and establishes the necessity of 2-edge connectivity for non-trivial computation.

Findings

Reliable simulation of algorithms in fully-defective networks is possible if the network is 2-edge connected.

Non-2-edge-connected networks cannot support non-trivial computations under full message corruption.

A construction of Robbins cycles in such networks enables communication despite total message corruption.

Abstract

We address fully-defective asynchronous networks, in which all links are subject to an unlimited number of alteration errors, implying that all messages in the network may be completely corrupted. Despite the possible intuition that such a setting is too harsh for any reliable communication, we show how to simulate any algorithm for a noiseless setting over any fully-defective setting, given that the network is 2-edge connected. We prove that if the network is not 2-edge connected, no non-trivial computation in the fully-defective setting is possible. The key structural property of 2-edge-connected graphs that we leverage is the existence of an oriented (non-simple) cycle that goes through all nodes [Robbins, 1939]. The core of our technical contribution is presenting a construction of such a Robbins cycle in fully-defective networks, and showing how to communicate over it despite total message corruption. These are obtained in a content-oblivious manner, since nodes must ignore the content of received messages.