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We consider the task of monitoring spatiotemporal phenomena in real-time bydeploying limited sampling resources at locations of interest irrevocably andwithout knowledge of future observations. This task can be modeled as aninstance of the classical secretary problem. Although this problem has beenstudied extensively in theoretical domains, existing algorithms require thatdata arrive in random order to provide performance guarantees. These algorithmswill perform arbitrarily poorly on data streams such as those encountered inrobotics and environmental monitoring domains, which tend to havespatiotemporal structure. We focus on the problem of selecting representativesamples from phenomena with periodic structure and introduce a novel sampleselection algorithm that recovers a near-optimal sample set according to anymonotone submodular utility function. We evaluate our algorithm on a seven-yearenvironmental dataset collected at the Martha's Vineyard Coastal Observatoryand show that it selects phytoplankton sample locations that are nearly optimalin an information-theoretic sense for predicting phytoplankton concentrationsin locations that were not directly sampled. The proposed periodic secretaryalgorithm can be used with theoretical performance guarantees in many real-timesensing and robotics applications for streaming, irrevocable sample selectionfrom periodic data streams.

Near-optimal irrevocable sample selection for periodic data streams with applications to marine robotics