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Round-Delayed Amnesiac Flooding

Oluwatobi Alafin, George B. Mertzios, Paul G. Spirakis

Abstract

We present a comprehensive analysis of Round-Delayed Amnesiac Flooding (RDAF), a variant of Amnesiac Flooding that introduces round-based asynchrony through adversarial delays. We establish fundamental properties of RDAF, including termination characteristics for different graph types and decidability results under various adversarial models. Our key contributions include: (1) a formal model of RDAF incorporating round-based asynchrony, (2) a proof that flooding always terminates on acyclic graphs despite adversarial delays, (3) a construction showing non-termination is possible on any cyclic graph, (4) a demonstration that termination is undecidable with arbitrary computable adversaries, and (5) the introduction of Eventually Periodic Adversaries (EPA) under which termination becomes decidable. These results enhance our understanding of flooding in communication-delay settings and provide insights for designing robust distributed protocols.

Round-Delayed Amnesiac Flooding

Abstract

We present a comprehensive analysis of Round-Delayed Amnesiac Flooding (RDAF), a variant of Amnesiac Flooding that introduces round-based asynchrony through adversarial delays. We establish fundamental properties of RDAF, including termination characteristics for different graph types and decidability results under various adversarial models. Our key contributions include: (1) a formal model of RDAF incorporating round-based asynchrony, (2) a proof that flooding always terminates on acyclic graphs despite adversarial delays, (3) a construction showing non-termination is possible on any cyclic graph, (4) a demonstration that termination is undecidable with arbitrary computable adversaries, and (5) the introduction of Eventually Periodic Adversaries (EPA) under which termination becomes decidable. These results enhance our understanding of flooding in communication-delay settings and provide insights for designing robust distributed protocols.

Paper Structure

This paper contains 14 sections, 15 theorems, 12 equations, 1 table.

Table of Contents

  1. Introduction
  2. Model Context and Novelty
  3. Our Contributions
  4. Organisation
  5. Related Work
  6. Model, Preliminaries and Notation
  7. Computational Model
  8. The RDAF Protocol
  9. System Evolution and Termination
  10. Termination Dichotomy
  11. Periodic Infinite Schedules
  12. Undecidability with Arbitrary Computable Adversaries
  13. Eventually Periodic Adversaries
  14. Conclusions and Open Problems

Key Result

lemma 1

All destination sets are empty at round $t$ if and only if flooding has terminated by round $t$. $\blacktriangleleft$$\blacktriangleleft$

Theorems & Definitions (38)

  • definition 1: Adversarial Delay Function
  • definition 2: Finite Delay Property
  • definition 3
  • lemma 1: Empty Destination Sets and Termination
  • proof
  • lemma 2
  • proof
  • lemma 3: Characterisation of Cyclic Pattern Disruption
  • proof
  • lemma 4: Non-disruption of Cyclic Pattern
  • ...and 28 more