Probabilistic estimation of network size and diameter

Determining the size of a network and its diameter are important functions in distributed systems, as there are a number of algorithms which rely on such parameters, or at least on estimates of those values. The Extrema Propagation technique allows the estimation of the size of a network in a fast, distributed and fault tolerant manner. The technique was previously studied in a simulation setting where rounds advance synchronously and where there is no message loss.This work presents two main contributions. The first, is the study of the Extrema Propagation technique under asynchronous rounds and integrated in the Network Friendly Epidemic Multicast (NeEM) framework. The second, is the evaluation of a diameter estimation technique associated with the Extrema Propagation. This study also presents a small enhancement the Extrema Propagation in terms of communication cost and points out some other possible enhancements. Results show that there is a clear trade-off between time and communication that must be considered when configuring the protocol—a faster convergence time implies a higher communication cost. Results also show that its possible to reduce the total communication cost by more than 18% using a simple approach. The diameter estimation technique is shown to have a relative error of less than10% even when using a small sample of nodes.
The authors would like to thank Jose Orlando Pereira and Nuno Carvalho for their help in the NeEM integration and testing. This work has been partially supported by FCT and POCI 2010, co-funded by the Portuguese Government and European Union in the FEDER Program.