Memory and communication efficient algorithm for decentralized counting of nodes in networks.

Arindam Saha,James A R Marshall,Andreagiovanni Reina

doi:10.1371/journal.pone.0259736

Arindam Saha, James A R Marshall + Show 1 more

Open Access

https://doi.org/10.1371/journal.pone.0259736

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Journal: PloS one	Publication Date: Nov 22, 2021
Citations: 3	License type: CC BY 4.0

Affiliation: University of Sheffield, Université Libre de Bruxelles

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 naïve 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.

Highlights

All decentralized systems share the common aspect of being comprised of a network of units that rely on local and partial information which they can gather from the subset of devices in their communication range
Deterministic algorithms provide the exact solution in a finite time, they may rely on stringent assumptions on the communication network topology
We compare the efficiency of the AnB algorithm against the All-2-All and the Single Tree (ST, [18]) algorithms in terms of three aspects: (a) the time required to compute the network size by every node, (b) the number of messages sent by all nodes, and (c) the minimum amount of memory required by each node to execute the algorithm

Summary

Introduction

All decentralized systems share the common aspect of being comprised of a network of units (which can be considered as graph nodes) that rely on local and partial information which they can gather from the subset of devices in their communication range (communication links can be represented as graph edges). We compare the efficiency of the AnB algorithm against the All-2-All and the Single Tree (ST, [18]) algorithms in terms of three aspects: (a) the time required to compute the network size by every node, (b) the number of messages sent by all nodes (i.e. the communication cost), and (c) the minimum amount of memory required by each node to execute the algorithm (i.e. the memory cost). The time and communication efficiency of the ST algorithm has been outlined by Bawa et al in [18] We updated their efficiency measures in order to include the changes required to allow all nodes to compute the network size. We conclude that the AnB algorithm is advantageous for applications with constrained or high-cost communication and memory, as confirmed by the results reported in Table 2 and Fig 4

Conclusion

Quorum sensing

Spontaneous hierarchy creation

Findings

Computation of other aggregate quantities