Distributed Computation of Exact Average Degree and Network Size in Finite Number of Steps under Quantized Communication

TL;DR

This paper introduces two novel distributed algorithms that compute the exact average degree and network size in finite steps using quantized communication, with nodes independently determining convergence.

Contribution

The algorithms are the first to achieve exact solutions under quantized communication and to compute network size exactly in finite steps without errors.

Findings

Algorithms compute exact average degree and network size.

Nodes can determine convergence and terminate independently.

No quantization or asymptotic errors in final results.

Abstract

We consider the problems of computing the average degree and the size of a given network in a distributed fashion under quantized communication. We present two distributed algorithms which rely on quantized operation (i.e., nodes process and transmit quantized messages), and are able to calculate the exact solutions in a finite number of steps. Furthermore, during the operation of our algorithms, each node is able to determine in a distributed manner whether convergence has been achieved and thus terminate its operation. To the best of the authors' knowledge these algorithms are the first to find the exact solutions under quantized communication (i.e., there is no error in the final calculation). Additionally, note that our network size calculation algorithm is the first in the literature which calculates the exact size of a network in a finite number of steps without introducing a final error. This error in other algorithms can be either due to quantization or asymptotic convergence. In our case, no error is introduced since the desired result is calculated in the form of a fraction involving a quantized numerator and a quantized denominator. Finally, we demonstrate the operation of our algorithms and their potential advantages.