Approximate Discontinuous Trajectory Hotspots

01/07/2019

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by   Ali Gholami Rudi, et al.

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A hotspot is an axis-aligned square of fixed side length s, the duration of the presence of an entity moving in the plane in which is maximised. An exact hotspot of a polygonal trajectory with n edges can be found in O(n^2). Defining a c-approximate hotspot as an axis-aligned square of side length cs, in which the duration of the entity's presence is no less than that of an exact hotspot, in this paper we present an algorithm to find a (1 + ϵ)-approximate hotspot of a polygonal trajectory with the time complexity O(nϕϵnϕϵ), where ϕ is the ratio of average trajectory edge length to s.