Related papers: Looking for Bird Nests: Identifying Stay Points wi…
In a nutshell, stay-points are locations that a person has stopped for some amount of time. Previous work depends mainly on stay-point identification methods using experimentally fine tuned threshold values. These behave well on their…
A hotspot of a moving entity is a region in which it spends a significant amount of time. Given the location of a moving object through a certain time interval, i.e. its trajectory, our goal is to find its hotspots. We consider…
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…
In this paper we study the problem of finding hotspots, i.e. regions in which a moving entity has spent a significant amount of time, for polygonal trajectories. The fastest optimal algorithm, due to Gudmundsson, van Kreveld, and Staals…
We discuss the properties of the residence time in presence of moving defects or obstacles for a particle performing a one dimensional random walk. More precisely, for a particle conditioned to exit through the right endpoint, we measure…
In this paper, we study the problem of map matching with travel time constraints. Given a sequence of $k$ spatio-temporal measurements and an embedded path graph with travel time costs, the goal is to snap each measurement to a close-by…
Consider two entities with constant but not necessarily equal velocities, moving on two given piece-wise linear trajectories inside a simple polygon $P$. The Trajectory Range Visibility problem deals with determining the sub-trajectories on…
Motivated by automated junction recognition in tracking data, we study a problem of placing a square or disc of fixed size in an arrangement of lines or line segments in the plane. We let distances among the intersection points of the lines…
The collective motion of a set of moving entities like people, birds, or other animals, is characterized by groups arising, merging, splitting, and ending. Given the trajectories of these entities, we define and model a structure that…
The requirement to trace and process moving objects in the contemporary era gradually increases since numerous applications quickly demand precise moving object locations. The Map-matching method is employed as a preprocessing technique,…
Stability is a fundamental notion in dynamical systems and control theory that, traditionally understood, describes asymptotic behavior of solutions around an equilibrium point. This notion may be characterized abstractly as continuity of a…
The classical multi-agent rendezvous problem asks for a deterministic algorithm by which $n$ points scattered in a plane can move about at constant speed and merge at a single point, assuming each point can use only the locations of the…
Let $\mathscr O$ be a set of $n$ disjoint obstacles in $\mathbb{R}^2$, $\mathscr M$ be a moving object. Let $s$ and $l$ denote the starting point and maximum path length of the moving object $\mathscr M$, respectively. Given a point $p$ in…
We show that a continuous map or a continuous flow on $\R^{n}$ with a certain recurrence relation must have a fixed point. Specifically, if there is a compact set W with the property that the forward orbit of every point in $\R^{n}$…
Given a set of N points, we have discovered an algorithm that can separate these points from one another by n-dimensional planes. Each point is chosen at random and put into a set S and planes which separate them are determined and put into…
We consider a repulsion actuator located in an $n$-sided convex environment full of point particles. When the actuator is activated, all the particles move away from the actuator. We study the problem of gathering all the particles to a…
Consider the continuum of points along the edges of a network, i.e., a connected, undirected graph with positive edge weights. We measure the distance between these points in terms of the weighted shortest path distance, called the network…
Stickiness is a well known phenomenon in which chaotic orbits expend an expressive amount of time in specific regions of the chaotic sea. This phenomenon becomes important when dealing with area-preserving open systems because, in this…
A segment (barrier) is specified on the plane, as well as depots, where the mobile devices (drones) can be placed. Each drone departs from its depot to the barrier, moves along the barrier and returns to its depot, traveling a path of a…
We present a numerical method to identify regions of phase space that are approximately retained in a mobile compact neighbourhood over a finite time duration. Our approach is based on spatio-temporal clustering of trajectory data. The main…