Related papers: Computing the Discrete Fr\'echet Distance in Subqu…
A stochastic leap-frog algorithm for the numerical integration of Brownian motion stochastic differential equations with multiplicative noise is proposed and tested. The algorithm has a second-order convergence of moments in a finite time…
The design of distributed gathering and convergence algorithms for tiny robots has recently received much attention. In particular, it has been shown that convergence problems can even be solved for very weak, \emph{oblivious} robots:…
Given sets $\mathcal{P}, \mathcal{Q} \subseteq \mathbb{R}^2$ of sizes $m$ and $n$ respectively, we are interested in the number of distinct distances spanned by $\mathcal{P} \times \mathcal{Q}$. Let $D(m, n)$ denote the minimum number of…
In this paper we present an interesting gadget based on the chain pair simplification problem under the discrete Fr\'echet distance (CPS-3F), which allows the construction of arbitrarily long paths that must be chosen in the simplification…
The problem of Approximate Nearest Neighbor (ANN) search is fundamental in computer science and has benefited from significant progress in the past couple of decades. However, most work has been devoted to pointsets whereas complex shapes…
We present a (combinatorial) algorithm with running time close to $O(n^d)$ for computing the minimum directed $L_\infty$ Hausdorff distance between two sets of $n$ points under translations in any constant dimension $d$. This substantially…
Unobtrusive monitoring of distances between people indoors is a useful tool in the fight against pandemics. A natural resource to accomplish this are surveillance cameras. Unlike previous distance estimation methods, we use a single,…
The Earth Mover's Distance is a popular similarity measure in several branches of computer science. It measures the minimum total edge length of a perfect matching between two point sets. The Earth Mover's Distance under Translation…
The \textit{biharmonic distance} (BD) is a fundamental metric that measures the distance of two nodes in a graph. It has found applications in network coherence, machine learning, and computational graphics, among others. In spite of BD's…
For most optimisation methods an essential assumption is the vector space structure of the feasible set. This condition is not fulfilled if we consider optimisation problems over the sphere. We present an algorithm for solving a special…
An important problem in geometric computing is defining and computing similarity between two geometric shapes, e.g. point sets, curves and surfaces, etc. Important geometric and topological information of many shapes can be captured by…
We design a deterministic algorithm that, given $n$ points in a \emph{typical} constant degree regular~graph, queries $O(n)$ distances to output a constant factor approximation to the average distance among those points, thus answering a…
The approximation of probability measures on compact metric spaces and in particular on Riemannian manifoldsby atomic or empirical ones is a classical task in approximation and complexity theory with a wide range of applications. Instead of…
The dynamic time warping (dtw) distance is an established tool for mining time series data. The DTW-Mean problem consists of computing a series which minimizes the so-called Fr\'echet function, that is, the sum of squared dtw-distances to a…
In this article, we propose tree edit distance with variables, which is an extension of the tree edit distance to handle trees with variables and has a potential application to measuring the similarity between mathematical formulas,…
For many shape analysis problems in computer vision and scientific imaging (e.g., computational anatomy, morphological cytometry), the ability to align two closed curves in the plane is crucial. In this paper, we concentrate on rigidly…
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…
Given a probability measure with density, Fermat distances and density-driven metrics are conformal transformations of the Euclidean metric that shrink distances in high density areas and enlarge distances in low density areas. Although…
Metric graphs are ubiquitous in science and engineering. For example, many data are drawn from hidden spaces that are graph-like, such as the cosmic web. A metric graph offers one of the simplest yet still meaningful ways to represent the…
It is an open question whether there exists a polynomial-time algorithm for computing the rotation distances between pairs of extended ordered binary trees. The problem of computing the rotation distance between an arbitrary pair of trees,…