Reductions in Distributed Computing Part II: k-Threshold Agreement Tasks

TL;DR

This paper introduces k-Threshold Agreement tasks in distributed computing, exploring their properties and relationships to Consensus, and establishing new reducibility and complexity results based on resiliency and process set size.

Contribution

It extends prior work by defining k-Threshold Agreement tasks, providing new irreducibility results, and developing oracle-based reductions involving weaker variants of previous reductions.

Findings

Higher resiliency increases task difficulty for fixed processes.

Smaller process sets make Consensus tasks harder for fixed resiliency.

New oracle-based reductions relate f-resiliency and wait-freedom.

Abstract

We extend the results of Part I by considering a new class of agreement tasks, the so-called k-Threshold Agreement tasks (previously introduced by Charron-Bost and Le Fessant). These tasks naturally interpolate between Atomic Commitment and Consensus. Moreover, they constitute a valuable tool to derive irreducibility results between Consensus tasks only. In particular, they allow us to show that (A) for a fixed set of processes, the higher the resiliency degree is, the harder the Consensus task is, and (B) for a fixed resiliency degree, the smaller the set of processes is, the harder the Consensus task is. The proofs of these results lead us to consider new oracle-based reductions, involving a weaker variant of the C-reduction introduced in Part I. We also discuss the relationship between our results and previous ones relating f-resiliency and wait-freedom.