Approximate Hotspots of Orthogonal Trajectories.
In this paper we study the problem of finding hotspots, i.e. regions in which a moving entity has spent a significant amount of time, for polygonal trajectories. The fastest optimal algorithm, due to Gudmundsson, van Kreveld, and Staals (2013) finds an axis-parallel square hotspot of fixed side length in $O(n^2)$. Limiting ourselves to the case in which the entity moves in a direction parallel either to the $x$ or the $y$-axis, We present an approximation algorithm with the time complexity $O(n \log^3 n)$ and approximation factor $1/2$.
Publisher URL: http://arxiv.org/abs/1710.05185
DOI: arXiv:1710.05185v3
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