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A common way of storing spatio-temporalinformation about mobile devices is in the form of a 3D (2D geography + time) trajectory. We argue that when cellular phones and Personal Digital Assistants become location-aware, the size of the spatio-temporal information generated may prohibit efficient processing. We propose to adopt a technique studied in computer graphics, namely line-simplification, as an approximation technique to solve this problem. Line simplification uses a distance function in producing the trajectory approximation. We postulate the desiderata for such a distance: it should be sound, namely the error of the answers to spatio-temporal queries must be bounded. We analyze several distances, and prove that some are sound in this sense for some types of queries, while others are not. Interestingly, not a single distance analyzed proves to be sound for all the common spatio-temporal queries, and …