Synchronization in Anonymous Networks Under Continuous Dynamics

Abstract: We present the $\kappa$-Synchronizer that works in non-synchronous dynamic networks under minimal assumptions. Our model allows continuous topological changes without any guarantee of eventual global or partial stabilization and assumes that nodes are anonymous. This deterministic synchronizer is the first to enable 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). In summary, we make the following contributions: (1) we extend the definition of synchronizers to networks with continuous arbitrary edge dynamics; (2) we present the first synchronizer from the semi-synchronous to the synchronous model in a network with continuous arbitrary edge dynamics; 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, since we show that the standard Pull model is not sufficient to allow for non-trivial synchronization in our scenario. The $\kappa$-Synchronizer operates with memory overhead at the nodes that is linear on the maximum node degree and logarithmic on the runtime of the underlying synchronous algorithm being simulated.