There currently exist two dominant strategies to reduce data sizes in analysis and visualization: reducing the precision of the data, e.g., through quantization, or reducing its resolution, e.g., by subsampling. Both have advantages and disadvantages and both face fundamental limits at which the reduced information ceases to be useful. The paper explores the additional gains that could be achieved by combining both strategies. In particular, we present a common framework that allows us to study the trade-off in reducing precision and/or resolution in a principled manner. We represent data reduction schemes as progressive streams of bits and study how various bit orderings such as by resolution, by precision, etc., impact the resulting approximation error across a variety of data sets as well as analysis tasks. Furthermore, we compute streams that are optimized for different tasks to serve as lower bounds on the achievable error. Scientific data management systems can use the results presented in this paper as guidance on how to store and stream data to make efficient use of the limited storage and bandwidth in practice.
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