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). Limiting ourselves to the case in which the entity moves in a direction parallel either to the x or the yaxis, We present an approximation algorithm with the time complexity O(n log n) and approximation factor 1/2.