Abstract
A stay region of a moving object is a region in which it spends a significant amount of time. Given the location of an object through a certain time interval, i.e. its trajectory, our goal is to find its stay regions. We consider axis-parallel square stay regions of fixed side length, which contain the longest continuous portion of the trajectory. We present an algorithm for answering time-windowed stay region queries, to find a stay region in any given time interval. The algorithm has an approximation factor of [Formula: see text] and answers each query with the time complexity [Formula: see text], in which [Formula: see text] is the number of vertices of the input trajectory. The time complexity of the preprocessing step of the algorithm is [Formula: see text]. We also present two approximation algorithms for finding stay regions of whole trajectories.
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