Smoothed analysis of dynamic networks

In this paper, we generalize the technique of smoothed analysis to apply to distributed algorithms in dynamic networks in which the network graph can change from round to round. Whereas standard smoothed analysis studies the impact of small random perturbations of input values on algorithm performance metrics, our proposed dynamic network version of smoothed analysis studies the impact of random perturbations of the underlying changing network topologies. Similar to the original application of smoothed analysis, our goal is to study whether known strong lower bounds in these models are robust or fragile: do they withstand small (random) perturbations, or do such deviations push the graphs far enough from a precise pathological instance to enable much better performance? Fragile lower bounds are likely not relevant for real-world deployment, while robust lower bounds represent a true difficulty caused by dynamic behavior. We apply this technique to three standard dynamic network problems with known strong worst-case lower bounds: random walks, flooding, and aggregation. We prove that these bounds provide a spectrum of robustness when subjected to smoothing—some are fragile (random walks), some are moderately fragile (flooding), and some are robust (aggregation).