Deterministic Fault-Tolerant Distributed Computing in Linear Time and Communication

Abstract

We develop deterministic algorithms for the problems of consensus, gossiping and checkpointing with nodes prone to failing. Distributed systems are modeled as synchronous complete networks. Failures are represented either as crashes or Byzantine faults with authentication. The algorithmic goal is to have both linear running time and linear amount of communication for as large an upper bound t on the number of faults as possible, with respect to the number of nodes n. For crash failures, these bounds of optimality are t = O(n / (log n)) for consensus and t = O(n / (log2 n)) for gossiping and checkpointing. For the model of Byzantine faults with authentication, we show how to reach consensus in both linear running time and communication for t = O(√n). We show how to implement the consensus algorithm for crash failures in the single-port model such as to preserve the range of t for which both the running time and communication are optimal. We prove a lower bound Ω (t+log n) on the running time of algorithms for each of the considered problems.