Smoothed Analysis of Dynamic Networks

TL;DR

This paper extends smoothed analysis to dynamic networks, examining how small random changes in network topology affect the robustness of known lower bounds for algorithms like random walks, flooding, and aggregation.

Contribution

It introduces a novel smoothed analysis framework for dynamic networks and classifies the robustness of lower bounds for key problems under perturbations.

Findings

Random walks are extremely fragile under smoothing.

Flooding exhibits moderate robustness.

Aggregation is highly robust to network perturbations.

Abstract

We generalize the technique of smoothed analysis to distributed algorithms in dynamic network models. Whereas standard smoothed analysis studies the impact of small random perturbations of input values on algorithm performance metrics, dynamic graph smoothed analysis studies the impact of random perturbations of the underlying changing network graph topologies. Similar to the original application of smoothed analysis, our goal is to study whether known strong lower bounds in dynamic network 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 extremely fragile (random walks), some are moderately fragile / robust (flooding), and some are extremely robust (aggregation).