A memory and communication efficient algorithm for decentralized counting of nodes in networks

TL;DR

This paper introduces a deterministic, distributed algorithm for counting nodes in a connected graph efficiently, requiring less memory and communication, and applicable to various network problems.

Contribution

A novel deterministic algorithm that efficiently counts nodes in a network with lower memory and communication costs than previous methods.

Findings

More efficient in memory and communication than previous algorithms

Comparable or better average-case time complexity

Applicable to other graph aggregation problems

Abstract

Node counting on a graph is subject to some fundamental theoretical limitations, yet a solution to such problems is necessary in many applications of graph theory to real-world systems, such as collective robotics and distributed sensor networks. Thus several stochastic and na{\"i}ve deterministic algorithms for distributed graph size estimation or calculation have been provided. Here we present a deterministic and distributed algorithm that allows every node of a connected graph to determine the graph size in finite time, if an upper bound on the graph size is provided. The algorithm consists in the iterative aggregation of information in local hubs which then broadcast it throughout the whole graph. The proposed node-counting algorithm is on average more efficient in terms of node memory and communication cost than its previous deterministic counterpart for node counting, and appears comparable or more efficient in terms of average-case time complexity. As well as node counting, the algorithm is more broadly applicable to problems such as summation over graphs, quorum sensing, and spontaneous hierarchy creation.