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Granular Synchrony

Neil Giridharan, Ittai Abraham, Natacha Crooks, Kartik Nayak, Ling Ren

TL;DR

A new timing model called granular synchrony is introduced that models the network as a mixture of synchronous, partially synchronous, and asynchronous communication links and serves as a unifying framework where current mainstream models are its special cases.

Abstract

Today's mainstream network timing models for distributed computing are synchrony, partial synchrony, and asynchrony. These models are coarse-grained and often make either too strong or too weak assumptions about the network. This paper introduces a new timing model called granular synchrony that models the network as a mixture of synchronous, partially synchronous, and asynchronous communication links. The new model is not only theoretically interesting but also more representative of real-world networks. It also serves as a unifying framework where current mainstream models are its special cases. We present necessary and sufficient conditions for solving crash and Byzantine fault-tolerant consensus in granular synchrony. Interestingly, consensus among $n$ parties can be achieved against $f \geq n/2$ crash faults or $f \geq n/3$ Byzantine faults without resorting to full synchrony.

Granular Synchrony

TL;DR

A new timing model called granular synchrony is introduced that models the network as a mixture of synchronous, partially synchronous, and asynchronous communication links and serves as a unifying framework where current mainstream models are its special cases.

Abstract

Today's mainstream network timing models for distributed computing are synchrony, partial synchrony, and asynchrony. These models are coarse-grained and often make either too strong or too weak assumptions about the network. This paper introduces a new timing model called granular synchrony that models the network as a mixture of synchronous, partially synchronous, and asynchronous communication links. The new model is not only theoretically interesting but also more representative of real-world networks. It also serves as a unifying framework where current mainstream models are its special cases. We present necessary and sufficient conditions for solving crash and Byzantine fault-tolerant consensus in granular synchrony. Interestingly, consensus among parties can be achieved against crash faults or Byzantine faults without resorting to full synchrony.
Paper Structure (22 sections, 19 theorems, 1 equation, 2 figures, 5 algorithms)

This paper contains 22 sections, 19 theorems, 1 equation, 2 figures, 5 algorithms.

Table of Contents

  1. Introduction
  2. Model and Definitions
  3. CFT Consensus in Granular Partial Synchrony
  4. Necessity
  5. Protocol
  6. Analysis
  7. CFT Consensus in Granular Asynchrony
  8. Necessity
  9. Protocol
  10. Analysis
  11. BFT Consensus in Granular Partial Synchrony
  12. Necessary
  13. Protocol
  14. Analysis
  15. Related Work
  16. ...and 7 more sections

Key Result

Theorem 1

Under granular partial synchrony, CFT consensus on a graph $G=(V, E)$ is solvable if and only if, regardless of which up to $f$ nodes are faulty, $\forall A \subseteq V$ with $|A| \geq n-f$, $\exists B \subseteq V$ with $|B| \geq f+1$ such that $A \rightarrow B$.

Figures (2)

  • Figure 1: Only synchronous links are shown in the figure for brevity. Faulty nodes are denoted in red with horns, and the correct nodes are denoted in gray. The figure shows the necessary and sufficient condition in theorem \ref{['thm:cft-gps']} being satisfied for (a)$n=4$, $f=2$, (b)$n=5$, $f=3$, and (c)$n=6$, $f=3$.
  • Figure 2: In this graph $n=4$ and $f=2$. Each edge represents a synchronous link and a missing edge represents an asynchronous link.

Theorems & Definitions (41)

  • Definition 1: Synchronous path
  • Definition 2
  • Definition 3: Path length, distance and diameter
  • Definition 4: Consensus
  • Theorem 1
  • proof
  • Lemma 1
  • proof
  • Theorem 2: Agreement
  • proof
  • ...and 31 more