Homology-based Distributed Coverage Hole Detection in Wireless Sensor Networks

TL;DR

This paper explores the use of homology theory, specifically Rips complexes, for distributed detection of coverage holes in wireless sensor networks, balancing accuracy and practicality.

Contribution

It introduces a homology-based distributed algorithm for coverage hole detection using Rips complexes and provides analytical bounds on detection accuracy.

Findings

Rips complex can detect most coverage holes with high accuracy.

The detection accuracy depends on the ratio of communication to sensing radii.

The proposed algorithm localizes about 99% of coverage holes in 99% of cases.

Abstract

Homology theory provides new and powerful solutions to address the coverage problems in wireless sensor networks (WSNs). They are based on algebraic objects, such as Cech complex and Rips complex. Cech complex gives accurate information about coverage quality but requires a precise knowledge of the relative locations of nodes. This assumption is rather strong and hard to implement in practical deployments. Rips complex provides an approximation of Cech complex. It is easier to build and does not require any knowledge of nodes location. This simplicity is at the expense of accuracy. Rips complex can not always detect all coverage holes. It is then necessary to evaluate its accuracy. This work proposes to use the proportion of the area of undiscovered coverage holes as performance criteria. Investigations show that it depends on the ratio between communication and sensing radii of a sensor. Closed-form expressions for lower and upper bounds of the accuracy are also derived. For those coverage holes which can be discovered by Rips complex, a homology-based distributed algorithm is proposed to detect them. Simulation results are consistent with the proposed analytical lower bound, with a maximum difference of 0.5%. Upper bound performance depends on the ratio of communication and sensing radii. Simulations also show that the algorithm can localize about 99% coverage holes in about 99% cases.