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arXiv · 1901.01763

Approximate Discontinuous Trajectory Hotspots

Ali Gholami Rudi
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Abstract

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 $O({nϕ\over ε} \log {nϕ\over ε})$, where $ϕ$ is the ratio of average trajectory edge length to $s$.

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Ali Gholami Rudi. 2019-01-07. Approximate Discontinuous Trajectory Hotspots. https://arxiv.org/abs/1901.01763

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