A Generic Framework for Impossibility Results in Time-Varying Graphs

We address highly dynamic distributed systems
modeled by time-varying graphs (TVGs). We are interested in
proof of impossibility results that often use informal arguments
about convergence. First, we provide a topological distance metric
over sets of TVGs to correctly define the convergence of TVG
sequences in such sets. Next, we provide a general framework that
formally proves the convergence of the sequence of executions
of any deterministic algorithm over TVGs of any convergent
sequence of TVGs. Finally, we illustrate the relevance of the
above result by proving that no deterministic algorithm exists to
compute the underlying graph of any connected-over-time TVG,
i.e., any TVG of the weakest class of long-lived TVGs.