Reaching Agreement Among $k$ out of $n$ Processes

TL;DR

This paper investigates the limits of reaching agreement among processes with crash failures, showing that communication can improve consensus in some cases but not others, especially with binary inputs.

Contribution

It characterizes when communication enables better agreement among processes under crash failures, highlighting the role of input diversity and system synchrony.

Findings

Communication improves agreement in some cases with multiple input values.

Deterministic asynchronous systems cannot improve agreement with binary inputs and crash failures.

The results delineate the boundaries of agreement possibilities in distributed systems.

Abstract

In agreement problems, each process has an input value and must choose a decision (output) value. Given $n\geq 2$ processes and $m \geq 2$ possible different input values, we want to design an agreement algorithm that enables as many processes as possible to decide on the (same) input value of one of the processes, in the presence of $t$ crash failures. Without communication, when each process simply decides on its input value, at least $\lceil (n-t)/m \rceil$ of the processes are guaranteed to always decide on the same value. Can we do better with communication? For some cases, for example when $m=2$, even in the presence of a single crash failure, the answer is negative in a deterministic asynchronous system where communication is either by using atomic read/write registers or by sending and receiving messages. The answer is positive in other cases.