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One of the biggest open problems in external memory data structures is the priority queue problem with DecreaseKey operations. If only Insert and ExtractMin operations need to be supported, one can design a comparison-based priority queue performing O((N/B) lg M/B N) I/Os over a sequence of N operations, where B is the disk block size in number of words and M is the main memory size in number of words. This matches the lower bound for comparison-based sorting and is hence optimal for comparison-based priority queues. However, if we also need to support DecreaseKeys, the performance of the best known priority queue is only O((N/B) lg 2 N) I/Os. The big open question is whether a degradation in performance really is necessary. We answer this question affirmatively by proving a lower bound of Ω((N/B) lg lg N B) I/Os for processing a sequence of N intermixed Insert, ExtraxtMin and DecreaseKey operations. Our lower bound is proved in the cell probe model and thus holds also for non-comparison-based priority queues.

A trajectory is a sequence of locations, each associated with a timestamp, describing the movement of a point. Trajectory data is becoming increasingly available and the size of recorded trajectories is getting larger. In this paper we study the problem of compressing planar trajectories such that the most common spatio-temporal queries can still be answered approximately after the compression has taken place. In the process, we develop an implementation of the Douglas-Peucker path-simplification algorithm which works efficiently even in the case where the polygonal path given as input is allowed to self-intersect. For a polygonal path of size n, the processing time is O(n log k n) for k = 2 or k = 3 depending on the type of simplification.

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