Approximate Hotspots of Orthogonal Trajectories

Article type: Research Article

Authors: Rudi, Ali Gholami^{; *}

Affiliations: Department of Electrical and Computer Engineering, Bobol Noshirvani University of Technology, Babol, Iran. gholamirudi@nit.ac.ir

Correspondence: [*] Address for correspondence: Department of Electrical and Computer Engineering, Bobol Noshirvani University of Technology, Babol, Iran.

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 log3 n) and approximation factor 1/2.

Keywords: Trajectory hotspots, Kinetic tournament, Computational geometry

DOI: 10.3233/FI-2019-1818

Journal: Fundamenta Informaticae, vol. 167, no. 4, pp. 271-285, 2019