Applied topology in static and dynamic sensor networks

In the study of sensor networks, many applications require topological analysis, and for some problems topological information is even sufficient. Here, we review how algebraic topology (and specifically simplicial homology theory) can be used as a general framework for detection of coverage holes in a coordinate-free sensor network. Extensions to distributed processing and localization algorithms are also reviewed, before progressing into discussion of a new way to apply algebraic topological methods to the analysis of coverage properties in dynamic sensor networks. Zigzag persistent homology is a recently developed method to track homological features (such as holes) over a sequence of spaces. This paper demonstrates the promise of this method for the identification of coverage holes in a time-varying coordinate-free sensor network, as well as the designation of coverage holes as significant or not, based on the length of time they are present in the sequence.