Approximate Hotspots of Orthogonal Trajectories.
In this paper we study the problem of finding hotspots of polygonal two-dimensional trajectories, i.e. regions in which a moving entity has spent a significant amount of time. The fastest optimal algorithm, due to Gudmundsson, van Kreveld, and Staals (2013), finds an axis-parallel square hotspot of fixed side length in $O(n^2)$. We present an approximation algorithm with the time complexity $O(n \log n)$ and approximation factor $1/4$ for orthogonal trajectories, in which the entity moves in a direction parallel either to the $x$ or to the $y$-axis. We also present a $1/4$-approximation algorithm for finding axis-parallel cube hotspots of fixed side length for orthogonal three-dimensional trajectories.
Publisher URL: http://arxiv.org/abs/1710.05185
DOI: arXiv:1710.05185v2
Keeping up-to-date with research can feel impossible, with papers being published faster than you'll ever be able to read them. That's where Researcher comes in: we're simplifying discovery and making important discussions happen. With over 19,000 sources, including peer-reviewed journals, preprints, blogs, universities, podcasts and Live events across 10 research areas, you'll never miss what's important to you. It's like social media, but better. Oh, and we should mention - it's free.
Researcher displays publicly available abstracts and doesn’t host any full article content. If the content is open access, we will direct clicks from the abstracts to the publisher website and display the PDF copy on our platform. Clicks to view the full text will be directed to the publisher website, where only users with subscriptions or access through their institution are able to view the full article.