Robust Node Estimation and Topology Discovery Algorithm in Large-Scale Wireless Sensor Networks

TL;DR

This paper presents a new statistical inference algorithm for estimating the number of nodes and their neighbors in large anonymous wireless sensor networks, achieving accuracy comparable to BLUE with limited queries.

Contribution

The work introduces a novel estimation algorithm that converges to BLUE and efficiently estimates network size and topology with minimal node queries.

Findings

Achieves 95% network estimation with small node queries.

Estimates converge to BLUE as queried nodes increase.

Effective in large-scale anonymous networks.

Abstract

This paper introduces a novel algorithm for cardinality, i.e., the number of nodes, estimation in large scale anonymous graphs using statistical inference methods. Applications of this work include estimating the number of sensor devices, online social users, active protein cells, etc. In anonymous graphs, each node possesses little or non-existing information on the network topology. In particular, this paper assumes that each node only knows its unique identifier. The aim is to estimate the cardinality of the graph and the neighbours of each node by querying a small portion of them. While the former allows the design of more efficient coding schemes for the network, the second provides a reliable way for routing packets. As a reference for comparison, this work considers the Best Linear Unbiased Estimators (BLUE). For dense graphs and specific running times, the proposed algorithm produces a cardinality estimate proportional to the BLUE. Furthermore, for an arbitrary number of iterations, the estimate converges to the BLUE as the number of queried nodes tends to the total number of nodes in the network. Simulation results confirm the theoretical results by revealing that, for a moderate running time, asking a small group of nodes is sufficient to perform an estimation of 95% of the whole network.