Distributed computing in asynchronous networks with byzantine edges

Abstract

A very basic property of fault-tolerant distributed computing, shown by Fischer, Lynch and Paterson, is that in the most general asynchronous network model, even in the presence of only one faulty processor it is impossible to achieve consensus. Thus, in the fault-tolerance context when processors may fail, the general model of distributed computing is anathema. In this work we investigate this totally asynchronous model in the presence of edge faults rather than processor ones.

Distributed computations in edge-faults models were previously investigated for more benign fault models, and our problem has been considered before but for the synchronous case; our goal here is to complete the investigation, showing a different behavior in the asynchronous case.

We classify possibility/impossibility (based on the resiliency), and compute the communication complexity for consensus in the asynchronous malicious-edge model on complete graphs. We get a message optimal algorithm as well. We employ consensus to get a general function evaluation in our model, and optimal evaluation protocol for semi-group computations. We also identify the required edge-connectivity for general networks, and show how to implement algorithms in these graphs based on connectivity conditions and algorithms.