Related papers: Topology and Routing Problems: The Circular Frame
A long-standing challenge is designing multi-scale structures with good connectivity between cells while optimizing each cell to reach close to the theoretical performance limit. We propose a new method for direct multi-scale topology…
We study data structure problems related to document indexing and pattern matching queries and our main contribution is to show that the pointer machine model of computation can be extremely useful in proving high and unconditional lower…
We describe a new algorithm to compute the geometric intersection number between two curves, given as edge vectors on an ideal triangulation. Most importantly, this algorithm runs in polynomial time in the bit-size of the two edge vectors.…
We propose a new method for segmentation-free joint estimation of orthogonal planes, their intersection lines, relationship graph and corners lying at the intersection of three orthogonal planes. Such unified scene exploration under…
A topological hyperplane is a subspace of R^n (or a homeomorph of it) that is topologically equivalent to an ordinary straight hyperplane. An arrangement of topological hyperplanes in R^n is a finite set H such that k topological…
We survey recent advances in algorithms for route planning in transportation networks. For road networks, we show that one can compute driving directions in milliseconds or less even at continental scale. A variety of techniques provide…
Computing optimal, collision-free trajectories for high-dimensional systems is a challenging problem. Sampling-based planners struggle with the dimensionality, whereas trajectory optimizers may get stuck in local minima due to inherent…
Real world data often lie on low-dimensional Riemannian manifolds embedded in high-dimensional spaces. This motivates learning degenerate normalizing flows that map between the ambient space and a low-dimensional latent space. However, if…
We study the computational complexity of routing multiple objects through a network in such a way that only few collisions occur: Given a graph $G$ with two distinct terminal vertices and two positive integers $p$ and $k$, the question is…
Given an unlabeled road map, we consider, from an algorithmic perspective, the cartographic problem to place non-overlapping road labels embedded in their roads. We first decompose the road network into logically coherent road sections,…
Path planning is a classic problem for autonomous robots. To ensure safe and efficient point-to-point navigation an appropriate algorithm should be chosen keeping the robot's dimensions and its classification in mind. Autonomous robots use…
A new methodological approach for the study of topology for shapes made of arrangements of lines, planes or solids is presented. Topologies for shapes are traditionally built on the classical theory of point-sets. In this paper, topologies…
Path finding is a well-studied problem in AI, which is often framed as graph search. Any-angle path finding is a technique that augments the initial graph with additional edges to build shorter paths to the goal. Indeed, optimal algorithms…
Controlling complex tasks in robotic systems, such as circular motion for cleaning or following curvy lines, can be dealt with using nonlinear vector fields. In this paper, we introduce a novel approach called rotational obstacle avoidance…
Optimal paths connecting randomly selected network nodes and fixed routers are studied analytically in the presence of non-linear overlap cost that penalizes congestion. Routing becomes increasingly more difficult as the number of selected…
The problem of finding a path between two points while avoiding obstacles is critical in robotic path planning. We focus on the feasibility problem: determining whether such a path exists. We model the robot as a query-specific rectangular…
Consider the problem of inverse scattering of time-harmonic point sources from an infinite, penetrable rough interface with bounded obstacles buried in the lower half-space, where the interface is assumed to be a local perturbation of a…
Generalist neural routing solvers have shown great potential in solving diverse vehicle routing problems (VRPs) with a unified model. However, existing solvers are typically limited to symmetric settings or degrade in performance when…
The understanding of the mechanisms driving vascular development is still limited. Techniques to generate vascular trees synthetically have been developed to tackle this problem. However, most algorithms are limited to single trees inside…
This article introduces a novel approach to constructing a topometric map that allows for efficient navigation and decision-making in mobile robotics applications. The method generates the topometric map from a 2D grid-based map. The…