Causality, Influence, and Computation in Possibly Disconnected Dynamic Networks

TL;DR

This paper investigates influence and computation in dynamic networks, introducing a minimal temporal connectivity condition that replaces traditional instantaneous connectivity, and explores its implications for network properties and protocols.

Contribution

It introduces a new temporal connectivity assumption for dynamic networks, establishing equivalences with traditional models and providing protocols for counting and network analysis.

Findings

Dynamic graphs with disconnected instances can have equivalent temporal connectivity to connected ones.

A termination criterion for influence propagation is established.

A protocol for counting nodes in the network is proposed.

Abstract

In this work, we study the propagation of influence and computation in dynamic distributed systems. We focus on broadcasting models under a worst-case dynamicity assumption which have received much attention recently. We drop for the first time in worst-case dynamic networks the common instantaneous connectivity assumption and require a minimal temporal connectivity. Our temporal connectivity constraint only requires that another causal influence occurs within every time-window of some given length. We establish that there are dynamic graphs with always disconnected instances with equivalent temporal connectivity to those with always connected instances. We present a termination criterion and also establish the computational equivalence with instantaneous connectivity networks. We then consider another model of dynamic networks in which each node has an underlying communication neighborhood and the requirement is that each node covers its local neighborhood within any time-window of some given length. We discuss several properties and provide a protocol for counting, that is for determining the number of nodes in the network.