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Persistent homology and zigzag persistent homology are techniques which trackthe homology over a sequence of spaces, outputting a set of intervalscorresponding to birth and death times of homological features in the sequence.This paper presents a method for choosing a homology class to correspond toeach of the intervals at each time point. For each homology class a specificrepresentative cycle is stored, with the choice of homology class andrepresentative cycle being both geometrically relevant and compatible with thebirth-death interval decomposition. After describing the method in detail andproving its correctness, we illustrate the utility of the method by applying itto the study of coverage holes in time-varying sensor networks.

Adaptive tracking of representative cycles in regular and zigzag persistent homology