Coordinate-free quantification of coverage in dynamic sensor networks

We present a methodology 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.In addition, 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. Graphical abstractDisplay Omitted HighlightsEach sensor has only a list of its neighboring sensors, with no coordinates, or inter-sensor distance information.Using these snapshots of local information, we describe the dynamic coverage properties of the network.Quantitative output is a weighted barcode, obtained using zigzag persistent homology.Estimated hole size and duration are encoded in this barcode.Method is able to distinguish between different sensor network mobility patterns.