Time-Windowed Contiguous Hotspot Queries
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A hotspot of a moving entity is a region in which it spends a significant amount of time. Given the location of a moving object through a certain time interval, i.e. its trajectory, our goal is to find its hotspots. We consider axis-parallel square hotspots of fixed side length, which contain the longest contiguous portion of the trajectory. Gudmundsson, van Kreveld, and Staals (2013) presented an algorithm to find a hotspot of a trajectory in O(n n), in which n is the number of vertices of the trajectory. We present an algorithm for answering time-windowed hotspot queries, to find a hotspot in any given time interval. The algorithm has an approximation factor of 1/2 and answers each query with the time complexity O(^2 n). The time complexity of the preprocessing step of the algorithm is O(n). When the query contains the whole trajectory, it implies an O(n) algorithm for finding approximate contiguous hotspots.
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