Related papers: Distance in the curve graph
We give necessary and sufficient topological conditions for a simple closed curve on a real rational surface to be approximable by smooth rational curves. We also study approximation by smooth rational curves with given complex…
To investigate the topological structure of Morse flows on the 2-disk we use the planar graphs as destinguished graph of the flow. We assume, that the flow is transversal to the boundary of the 2-disk. We give a list of all planar graph…
We prove that a graph on up to 9 vertices is a unit-distance graph if and only if it does not contain one of 74 so-called minimal forbidden graphs. This extends the work of Chilakamarri and Mahoney (1995), who provide a similar…
The Frechet distance is often used to measure distances between paths, with applications in areas ranging from map matching to GPS trajectory analysis to handwriting recognition. More recently, the Frechet distance has been generalized to a…
We introduce an estimator for the curvature of curves and surfaces by using finite sample points drawn from sampling a probability distribution that has support on the curve or surface. First we give an algorithm for estimation of the…
We state and prove some counting formulas relating to cliques in the distant graphs of projective lines over finite rings. As a preliminary to this, we prove a decomposition theorem for the graphs in terms of the direct-product…
In machine learning and particularly in topological data analysis, $\epsilon$-graphs are important tools but are generally hard to compute as the distance calculation between n points takes time O(n^2) classically. Recently, quantum…
In this paper we study the geometry of graph spaces endowed with a special class of graph edit distances. The focus is on geometrical results useful for statistical pattern recognition. The main result is the Graph Representation Theorem.…
Geometry and topology have generated impacts far beyond their pure mathematical primitive, providing a solid foundation for many applicable tools. Typically, real-world data are represented as vectors, forming a linear subspace for a given…
We give an accessible introduction and elaboration on the methods used in obtaining a geodesic, which is the curve of shortest length connecting two points lying on the surface of a function. This is found through computing what's known as…
In this paper, we leverage the properties of non-Euclidean Geometry to define the Geodesic distance (GD) on the space of statistical manifolds. The Geodesic distance is a real and intuitive similarity measure that is a good alternative to…
A {\em faithful (unit) distance graph} in $\mathbb{R}^d$ is a graph whose set of vertices is a finite subset of the $d$-dimensional Euclidean space, where two vertices are adjacent if and only if the Euclidean distance between them is…
The area distance to a convex plane curve is an important concept in computer vision. In this paper we describe a strong link between area distances and improper affine spheres. This link makes possible a better understanding of both…
In this paper we offer a metric similar to graph edit distance which measures the distance between two (possibly infinite)weighted graphs with finite norm (we define the norm of a graph as the sum of absolute values of its edges). The main…
We introduce a new graph minimization method, in which it is required to preserve some graph property and there is an effective procedure for checking this property. We applied this method to minimize 5-chromatic unit-distance graphs and…
In this paper we give a survey of methods used to calculate values of resistance distance (also known as effective resistance) in graphs. Resistance distance has played a prominent role not only in circuit theory and chemistry, but also in…
We present an algorithm for computing curves and families of curves of prescribed degree and geometric genus on real rational surfaces.
We define a (pseudo-)distance between graphs based on the spectrum of the normalized Laplacian, which is easy to compute or to estimate numerically. It can therefore serve as a rough classification of large empirical graphs into families…
We show that for every simple closed curve \alpha, the extremal length and the hyperbolic length of \alpha are quasi-convex functions along any Teichmuller geodesic. As a corollary, we conclude that, in Teichmuller space equipped with the…
The fine curve graph of a surface is a graph whose vertices are essential simple closed curves and whose edges connect disjoint curves. Following a rich history of hyperbolicity of various graphs associated to surfaces, the fine curve graph…