Coordinate-Free Quantification of Coverage in Dynamic Sensor Networks

TL;DR

This paper introduces a topology-based framework using zigzag persistent homology to analyze and visualize coverage dynamics in sensor networks over time, including hole tracking and size estimation.

Contribution

It develops a novel method combining computational topology and barcode analysis to quantify and visualize coverage in dynamic sensor networks.

Findings

Effective tracking of coverage holes over time.

Quantitative estimates of coverage hole sizes.

A weighted barcode for visualizing coverage dynamics.

Abstract

We present a novel set of methods for analyzing coverage properties in dynamic sensor networks. The dynamic sensor network under consideration is studied through a series of snapshots, and is represented by a sequence of simplicial complexes, built from the communication graph at each time point. A method from computational topology called zigzag persistent homology takes this sequence of simplicial complexes as input, and returns a `barcode' containing the birth and death times of homological features in this sequence. We derive useful statistics from this output for analyzing time-varying coverage properties. Further, we propose a method which returns specific representative cycles for these homological features, at each point along the birth-death intervals. These representative cycles are then used to track coverage holes in the network, and obtain size estimates for individual holes at each time point. A weighted barcode, incorporating the size information, is then used as a visual and quantitative descriptor of the dynamic network coverage.