Related papers: An Efficient Solution to the 2D Visibility Problem…
Finding interesting symmetrical topological structures in high-dimensional systems is an important problem in statistical machine learning. Limited amount of available high-dimensional data and its sensitivity to noise pose computational…
We propose a novel learning based algorithm to generate efficient and physically plausible sampling patterns in MRI. This method has a few advantages compared to recent learning based approaches: i) it works off-the-grid and ii) allows to…
In this article we consider the problem of finding the visibility set from a given point when the obstacles are represented as the level set of a given function. Although the visibility set can be computed efficiently by ray tracing, there…
An optimal data partitioning in parallel & distributed implementation of clustering algorithms is a necessary computation as it ensures independent task completion, fair distribution, less number of affected points and better & faster…
We introduce a greedy algorithm optimizing arrangements of lines with respect to a property. We apply this algorithm to the case of simpliciality: it recovers all known simplicial arrangements of lines in a very short time and also produces…
Many disciplines of science and engineering deal with problems related to compositions, ranging from chemical compositions in materials science to portfolio compositions in economics. They exist in non-Euclidean simplex spaces, causing many…
A key challenge in fast ground robot navigation in 3D terrain is balancing robot speed and safety. Recent work has shown that 2.5D maps (2D representations with additional 3D information) are ideal for real-time safe and fast planning.…
For a fixed virtual scene (=collection of simplices) S and given observer position p, how many elements of S are weakly visible (i.e. not fully occluded by others) from p? The present work explores the trade-off between query time and…
Given a simple polygon $ \mathcal {P} $ of $ n $ vertices in the Plane. We study the problem of computing the visibility area from a given viewpoint $ q $ inside $ \mathcal {P} $ where only sub-linear variables are allowed for working…
We study a path planning problem where the possible move actions are represented as a finite set of motion primitives aligned with the grid representation of the environment. That is, each primitive corresponds to a short…
We consider the classical Minimum Balanced Cut problem: given a graph $G$, compute a partition of its vertices into two subsets of roughly equal volume, while minimizing the number of edges connecting the subsets. We present the first {\em…
As the discretization error for the solution of a partial differential equation (PDE) decreases, the precision required to store the corresponding coefficients naturally increases. Storing the solution's finite element coefficients…
We revisit a classical graph-theoretic problem, the \textit{single-source shortest-path} (SSSP) problem, in weighted unit-disk graphs. We first propose an exact (and deterministic) algorithm which solves the problem in $O(n \log^2 n)$ time…
Navigating cluttered environments is a challenging task for any mobile system. Existing approaches for ground-based mobile systems primarily focus on small wheeled robots, which face minimal constraints with overhanging obstacles and cannot…
Problems from graph drawing, spectral clustering, network flow and graph partitioning can all be expressed in terms of graph Laplacian matrices. There are a variety of practical approaches to solving these problems in serial. However, as…
Let $s$ be a point in a polygonal domain $\mathcal{P}$ of $h-1$ holes and $n$ vertices. We consider a quickest visibility query problem. Given a query point $q$ in $\mathcal{P}$, the goal is to find a shortest path in $\mathcal{P}$ to move…
In this paper, we address the numerical solution of the Optimal Transport Problem on undirected weighted graphs, taking the shortest path distance as transport cost. The optimal solution is obtained from the long-time limit of the gradient…
We study the problem of clustering networks whose nodes have imputed or physical positions in a single dimension, for example prestige hierarchies or the similarity dimension of hyperbolic embeddings. Existing algorithms, such as the…
We present TOPGN, a novel method for real-time transparent obstacle detection for robot navigation in unknown environments. We use a multi-layer 2D grid map representation obtained by summing the intensities of lidar point clouds that lie…
The Poisson equation is commonly encountered in engineering, for instance in computational fluid dynamics (CFD) where it is needed to compute corrections to the pressure field to ensure the incompressibility of the velocity field. In the…