Synchronization in Anonymous Networks Under Arbitrary Dynamics

TL;DR

This paper introduces the $oldsymbol{ ext{ extdelta}}$-Synchronizer, a deterministic method enabling nodes in highly dynamic, anonymous networks to simulate synchronous algorithms without global clocks or stable connectivity, under minimal assumptions.

Contribution

It extends synchronizer definitions to arbitrary edge dynamics, presents the first semi-synchronous to synchronous synchronizer in such networks, and demonstrates practical applications.

Findings

Operates with logarithmic memory overhead relative to runtime

Works under weakly-fair node activation schedulers

Requires an extended communication model with 1-bit multi-writer registers

Abstract

We present the $\delta$-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 $\delta$-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.