Abstract
We generalize the technique of smoothed analysis to distributed algorithms in dynamic networks. 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).
M. Dinitz—Supported in part by NSF grant #1464239.
J. Fineman—Supported in part by NSF grants CCF-1218188 and CCF-1314633.
S. Gilbert—Supported in part by Singapore MOE Tier 2 ARC project 2014-T2-1-157.
C. Newport—Supported in part by NSF grant CCF 1320279.
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Dinitz, M., Fineman, J., Gilbert, S., Newport, C. (2015). Smoothed Analysis of Dynamic Networks. In: Moses, Y. (eds) Distributed Computing. DISC 2015. Lecture Notes in Computer Science(), vol 9363. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48653-5_34
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DOI: https://doi.org/10.1007/978-3-662-48653-5_34
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