Related papers: Trajectory Range Visibility
Point location problems for $n$ points in $d$-dimensional Euclidean space (and $\ell_p$ spaces more generally) have typically had two kinds of running-time solutions: * (Nearly-Linear) less than $d^{poly(d)} \cdot n \log^{O(d)} n$ time, or…
The Straightness is a measure designed to characterize a pair of vertices in a spatial graph. It is defined as the ratio of the Euclidean distance to the graph distance between these vertices. It is often used as an average, for instance to…
We study the classical problem of computing geometric thickness, i.e., finding a straight-line drawing of an input graph and a partition of its edges into as few parts as possible so that each part is crossing-free. Since the problem is…
Identifying relations between objects is central to understanding the scene. While several works have been proposed for relation modeling in the image domain, there have been many constraints in the video domain due to challenging dynamics…
We study the problem of planning paths for $p$ distinguishable pebbles (robots) residing on the vertices of an $n$-vertex connected graph with $p \le n$. A pebble may move from a vertex to an adjacent one in a time step provided that it…
Robots that share an environment with humans may communicate their intent using a variety of different channels. Movement is one of these channels and, particularly in manipulation tasks, intent communication via movement is called…
Given a graph $G$ and two vertices $s$ and $t$ in it, {\em graph reachability} is the problem of checking whether there exists a path from $s$ to $t$ in $G$. We show that reachability in directed layered planar graphs can be decided in…
Obstacle avoidance from monocular images is a challenging problem for robots. Though multi-view structure-from-motion could build 3D maps, it is not robust in textureless environments. Some learning based methods exploit human demonstration…
The problem of maneuvering a vehicle through a race course in minimum time requires computation of both longitudinal (brake and throttle) and lateral (steering wheel) control inputs. Unfortunately, solving the resulting nonlinear optimal…
Query evaluation on probabilistic databases is generally intractable (#P-hard). Existing dichotomy results have identified which queries are tractable (or safe), and connected them to tractable lineages. In our previous work, using…
We study a family of reachability problems under waiting-time restrictions in temporal and vertex-colored temporal graphs. Given a temporal graph and a set of source vertices, we find the set of vertices that are reachable from a source via…
Present article deals with trajectorial intersections in linear fractional systems ('systems'). We propose a classification of intersections of trajectories in three classes viz. trajectories intersecting at same time(EIST), trajectories…
A wide range of physical problems can be described by randomly-oriented linear trajectories, including any system of objects, organisms, particles, or rays that follow a linear path. Dependent upon the particular random variables that…
Trajectory-based spatiotemporal entity linking is to match the same moving object in different datasets based on their movement traces. It is a fundamental step to support spatiotemporal data integration and analysis. In this paper, we…
Among fundamental problems in the context of distributed computing by autonomous mobile entities, one of the most representative and well studied is {\sc Point Convergence}: given an arbitrary initial configuration of identical entities,…
In this paper, we revisit the problem of classical \textit{meeting times} of random walks in graphs. In the process that two tokens (called agents) perform random walks on an undirected graph, the meeting times are defined as the expected…
Obstacle representations of graphs have been investigated quite intensely over the last few years. We focus on graphs that can be represented by a single obstacle. Given a (topologically open) polygon $C$ and a finite set $P$ of points in…
This paper considers the robustness of an uncertain nonlinear system along a finite-horizon trajectory. The uncertain system is modeled as a connection of a nonlinear system and a perturbation. The analysis relies on three ingredients.…
We propose a global constructibility analysis for a vehicle moving on a planar surface. Assuming that the vehicle follows a trajectory that can be uniquely identified by the sequence of control inputs and by some intermittent ranging…
Given a line segment $I=[0,L]$, the so-called barrier, and a set of $n$ sensors with varying ranges positioned on the line containing $I$, the barrier coverage problem is to move the sensors so that they cover $I$, while minimising the…