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Synchronization in Anonymous Networks Under Arbitrary Dynamics

Rida Bazzi, Cameron Bickley, Anya Chaturvedi, Andréa W. Richa, Peter Vargas

TL;DR

This work addresses synchronization in anonymous networks subject to arbitrary, non-stabilizing edge dynamics. It introduces the delta-Synchronizer, a deterministic mechanism that converts synchronous dynamic-network algorithms into correct semi-synchronous executions without node identifiers or global timing, by using a two-phase Handshake/ExecuteSynch protocol and a 1-bit multi-writer register extension on edge-ports. The authors prove correctness, non-triviality, and liveness, and show that the approach preserves all synchronous outcomes while enabling finite-time termination under weak fairness. They also demonstrate tangible applications, such as porting spanning-forest maintenance to semi-synchronous environments and accelerating minority dynamics, highlighting the practical impact for highly dynamic networks.

Abstract

We present the $δ$-Synchronizer, which works in non-synchronous dynamic networks under minimal assumptions. Our model allows for arbitrary topological changes without any guarantee of eventual global or partial stabilization and assumes that nodes are anonymous. This deterministic synchronizer is the first that enables nodes to simulate a dynamic network synchronous algorithm for executions in a semi-synchronous dynamic environment under a weakly-fair node activation scheduler, despite the absence of a global clock, node ids, persistent connectivity or any assumptions about the edge dynamics (in both the synchronous and semi-synchronous environments). We make the following contributions: (1) we extend the definition of synchronizers to networks with arbitrary edge dynamics; (2) we present the first synchronizer from the semi-synchronous to the synchronous model in such networks; and (3) we present non-trivial applications of the proposed synchronizer to existing algorithms. We assume an extension of the Pull communication model by adding a single 1-bit multi-writer atomic register at each edge-port of a node. We show that this extension is needed and that synchronization in our setting is not possible without it. The $δ$-Synchronizer operates with a multiplicative memory overhead at the nodes that is asymptotically logarithmic on the runtime of the underlying synchronous algorithm being simulated-in particular, it is logarithmic for polynomial-time synchronous algorithms.

Synchronization in Anonymous Networks Under Arbitrary Dynamics

TL;DR

This work addresses synchronization in anonymous networks subject to arbitrary, non-stabilizing edge dynamics. It introduces the delta-Synchronizer, a deterministic mechanism that converts synchronous dynamic-network algorithms into correct semi-synchronous executions without node identifiers or global timing, by using a two-phase Handshake/ExecuteSynch protocol and a 1-bit multi-writer register extension on edge-ports. The authors prove correctness, non-triviality, and liveness, and show that the approach preserves all synchronous outcomes while enabling finite-time termination under weak fairness. They also demonstrate tangible applications, such as porting spanning-forest maintenance to semi-synchronous environments and accelerating minority dynamics, highlighting the practical impact for highly dynamic networks.

Abstract

We present the -Synchronizer, which works in non-synchronous dynamic networks under minimal assumptions. Our model allows for arbitrary topological changes without any guarantee of eventual global or partial stabilization and assumes that nodes are anonymous. This deterministic synchronizer is the first that enables nodes to simulate a dynamic network synchronous algorithm for executions in a semi-synchronous dynamic environment under a weakly-fair node activation scheduler, despite the absence of a global clock, node ids, persistent connectivity or any assumptions about the edge dynamics (in both the synchronous and semi-synchronous environments). We make the following contributions: (1) we extend the definition of synchronizers to networks with arbitrary edge dynamics; (2) we present the first synchronizer from the semi-synchronous to the synchronous model in such networks; and (3) we present non-trivial applications of the proposed synchronizer to existing algorithms. We assume an extension of the Pull communication model by adding a single 1-bit multi-writer atomic register at each edge-port of a node. We show that this extension is needed and that synchronization in our setting is not possible without it. The -Synchronizer operates with a multiplicative memory overhead at the nodes that is asymptotically logarithmic on the runtime of the underlying synchronous algorithm being simulated-in particular, it is logarithmic for polynomial-time synchronous algorithms.

Paper Structure

This paper contains 7 sections, 10 theorems, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Model
  4. The $\delta$-Synchronizer
  5. Analysis
  6. Applications and Extensions
  7. Conclusion and Future Work

Key Result

lemma 1

For any two nodes $u$ and $v$, $u$ perceives the undirected edge $(u,v)$ as present in phase $i$ (i.e., $(u,v) \in H_i$) if and only if $v$ also perceives $(v,u)\in H_i$. In other words, $u\in v.F^i$ if and only if $v\in u.F^i$. Moreover, if $t$ is the stage when node $v$ executes ExecuteSynch for

Theorems & Definitions (11)

  • definition 1: Valid Persistent Neighbors
  • lemma 1
  • lemma 2
  • theorem 1: Correctness
  • theorem 2: Weak non-triviality
  • lemma 3
  • theorem 3: Finite termination
  • corollary 1
  • theorem 4
  • corollary 2
  • ...and 1 more