Counting in Practical Anonymous Dynamic Networks is Polynomial

TL;DR

This paper demonstrates through simulations that an exact counting protocol in anonymous dynamic networks operates in polynomial time across various challenging topologies, making it practical for real-world applications.

Contribution

It provides the first experimental validation that an exact counting protocol runs in polynomial time in diverse anonymous dynamic network scenarios.

Findings

Protocol is polynomial in all tested network topologies

Topology changes impact information dissemination

Practical applications are feasible with predictable topology changes

Abstract

Anonymous Dynamic Networks is a harsh computational environment due to changing topology and lack of identifiers. Computing the size of the network, a problem known as Counting, is particularly challenging because messages received cannot be tagged to a specific sender. Previous works on Counting in Anonymous Dynamic Networks do not provide enough guarantees to be used in practice. Indeed, they either compute only an upper bound on the network size that may be as bad as exponential, or guarantee only double-exponential running time, or do not terminate, or guarantee only eventual termination without running-time guarantees. Faster experimental protocols do not guarantee the correct count. Recently, we presented the first Counting protocol that computes the exact count with exponential running-time guarantees. The protocol requires the presence of one leader node and knowledge of any upper bound Delta on the maximum number of neighbors that any node will ever have. In the present work, we complement the latter theoretical study evaluating the performance of such protocol in practice. We tested a variety of network topologies that may appear in practice, including extremal cases such as trees, paths, and continuously changing topologies. We also tested networks that temporarily are not connected. Our simulations showed that the protocol is polynomial for all the inputs tested, paving the way to use it in practical applications where topology changes are predictable. The simulations also provided insight on the impact of topology changes on information dissemination. To the best of our knowledge, this is the first experimental study that shows the possibility of computing the exact count in polynomial time in a variety of Anonymous Dynamic Networks that are worse than expected in practice.