Related papers: Efficient geodesics and an effective algorithm for…
We present a framework for embedding graph structured data into a vector space, taking into account node features and topology of a graph into the optimal transport (OT) problem. Then we propose a novel distance between two graphs, named…
In this paper, we consider enumeration of geodesics on a polyhedron, where a geodesic means locally-shortest path between two points. Particularly, we consider the following preprocessing problem: given a point $s$ on a polyhedral surface…
This paper presents the first polynomial time algorithm to compute geodesics in a CAT(0) cubical complex in general dimension. The algorithm is a simple iterative method to update breakpoints of a path joining two points using Miller, Owen…
Given a simple polygon $P$ and a set $Q$ of points contained in $P$, we consider the geodesic $k$-center problem where we want to find $k$ points, called \emph{centers}, in $P$ to minimize the maximum geodesic distance of any point of $Q$…
We give bounds on geodesic distances on the Stiefel manifold, derived from new geometric insights. The considered geodesic distances are induced by the one-parameter family of Riemannian metrics introduced by H\"uper et al. (2021), which…
The algorithms given in Karney, J. Geodesy 87, 43-55 (2013), to compute geodesics on terrestrial ellipsoids are extended to apply to ellipsoids of revolution with arbitrary eccentricity. For the direct and inverse geodesic problems, this…
We investigate quantifying the difference between two hybrid dynamical systems under noise and initial-state uncertainty. While the set of traces for these systems is infinite, it is possible to symbolically approximate trace sets using…
New finite element methods are proposed for elliptic interface problems in one and two dimensions. The main motivation is not only to get an accurate solution but also an accurate first order derivative at the interface (from each side).…
Metrics on the space of sets of trajectories are important for scientists in the field of computer vision, machine learning, robotics, and general artificial intelligence. However, existing notions of closeness between sets of trajectories…
We propose and study a set of algorithms for discovering community structure in networks -- natural divisions of network nodes into densely connected subgroups. Our algorithms all share two definitive features: first, they involve iterative…
Motion planning for vehicles under the influence of flow fields can benefit from the idea of streamline-based planning, which exploits ideas from fluid dynamics to achieve computational efficiency. Important to such planners is an efficient…
We give an efficient algorithm for robustly clustering of a mixture of two arbitrary Gaussians, a central open problem in the theory of computationally efficient robust estimation, assuming only that the the means of the component Gaussians…
Based on a local approximation of the Riemannian distance on a manifold by a computationally cheap dissimilarity measure, a time discrete geodesic calculus is developed, and applications to shape space are explored. The dissimilarity…
There are no known efficient algorithms to calculate distance in the one-skeleta of associahedra, a problem that is equivalent to finding rotation distance between rooted binary trees or the flip distance between polygonal triangulations.…
The matching distance is a computationally tractable topological measure to compare multi-filtered simplicial complexes. We design efficient algorithms for approximating the matching distance of two bi-filtered complexes to any desired…
We propose a new algorithm for finding the center of a graph, as well as the rank of each node in the hierarchy of distances to the center. In other words, our algorithm allows to partition the graph according to nodes distance to the…
Trajectories that capture object movement have numerous applications, in which similarity computation between trajectories often plays a key role. Traditionally, the similarity between two trajectories is quantified by means of heuristic…
In many robotics applications, it is necessary to compute not only the distance between the robot and the environment, but also its derivative - for example, when using control barrier functions. However, since the traditional Euclidean…
Manifolds discovered by machine learning models provide a compact representation of the underlying data. Geodesics on these manifolds define locally length-minimising curves and provide a notion of distance, which are key for reduced-order…
Large graphs are difficult to represent, visualize, and understand. In this paper, we introduce "gate graph" - a new approach to perform graph simplification. A gate graph provides a simplified topological view of the original graph.…