A Generic Framework for Impossibility Results in Time-Varying Graphs

Abstract

We address highly dynamic distributed systems modelled 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.