Time-Windowed Contiguous Hotspot Queries

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 log n), in which n is the number of vertices of the trajectory. We present an algorithm for answering timewindowed 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(log 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.