Approximate Hotspots of Orthogonal Trajectories

Abstract

We study the problem of finding hotspots, i.e. regions, in which a moving entity spends a significant amount of time, for polygonal trajectories. The fastest exact algorithm, due to Gudmundsson, van Kreveld, and Staals (2013) finds an axis-parallel square hotspot of fixed side length in O(n²) for a trajectory with n edges. Limiting ourselves to the case in which the entity moves in a direction parallel either to the x or to the y-axis, we present an approximation algorithm with the time complexity O(n log³n) and approximation factor 1/2.