Related papers: On Flipping the Fr\'{e}chet distance
We provide a linear time algorithm to determine the flip distance between two plane spanning paths on a point set in convex position. At the same time, we show that the happy edge property does not hold in this setting. This has to be seen…
We present new approximation results on curve simplification and clustering under Fr\'echet distance. Let $T = \{\tau_i : i \in [n] \}$ be polygonal curves in $R^d$ of $m$ vertices each. Let $l$ be any integer from $[m]$. We study a…
Let $G$ be a connected graph. The average distance of a vertex $v$ of $G$ is the arithmetic mean of the distances from $v$ to all other vertices of $G$. The proximity and remoteness of $G$ are defined as the minimum and maximum,…
We develop a transfer matrix formalism to visualize the framing of discrete piecewise linear curves in three dimensional space. Our approach is based on the concept of an intrinsically discrete curve, which enables us to more effectively…
Detecting commuting patterns or migration patterns in movement data is an important problem in computational movement analysis. Given a trajectory, or set of trajectories, this corresponds to clustering similar subtrajectories. We study…
Computing the diameter of a graph, i.e. the largest distance, is a fundamental problem that is central in fine-grained complexity. In undirected graphs, the Strong Exponential Time Hypothesis (SETH) yields a lower bound on the time vs.…
The distance on a set is a comparative function. The smaller the distance between two elements of that set, the closer, or more similar, those elements are. Fr\'echet axiomatized the distance into what is today known as a metric. In this…
We provide a new angle and obtain new results on a class of metrics on length-normalized curves in $d$ dimensions, represented by their unit tangents expressed as a function of arc-length, which are functions from the unit interval to the…
It is unlikely that the discrete Fr\'echet distance between two curves of length $n$ can be computed in strictly subquadratic time. We thus consider the setting where one of the curves, $P$, is known in advance. In particular, we wish to…
To characterize the location (mean, median) of a set of graphs, one needs a notion of centrality that is adapted to metric spaces, since graph sets are not Euclidean spaces. A standard approach is to consider the Frechet mean. In this work,…
We introduce an orientation-preserving landmark-based distance for continuous curves, which can be viewed as an alternative to the \Frechet or Dynamic Time Warping distances. This measure retains many of the properties of those measures,…
We consider mappings satisfying an upper bound for the distortion of families of curves. We establish lower bounds for the distortion of distances under such mappings. As applications, we obtain theorems on the discreteness of the limit…
The Procrustes distance is used to quantify the similarity or dissimilarity of (3-dimensional) shapes, and extensively used in biological morphometrics. Typically each (normalized) shape is represented by N landmark points, chosen to be…
We study the Fr\'echet queries problem. It is a data structure problem, where we are given a set $S$ of $n$ polygonal curves and a distance threshold $\rho$. The data structure should support queries with a polygonal curve $q$ for the…
In algorithms for finite metric spaces, it is common to assume that the distance between two points can be computed in constant time, and complexity bounds are expressed only in terms of the number of points of the metric space. We…
Data consisting of a graph with a function mapping into $\mathbb{R}^d$ arise in many data applications, encompassing structures such as Reeb graphs, geometric graphs, and knot embeddings. As such, the ability to compare and cluster such…
A new class of statistical deformable models is introduced to study high-dimensional curves or images. In addition to the standard measurement error term, these deformable models include an extra error term modeling the individual…
Biological processes like growth, aging, and disease progression are generally studied with follow-up scans taken at different time points, i.e., with image time series (TS) based analysis. Comparison between TS representing a biological…
Fr\'echet means, conceptually appealing, generalize the Euclidean expectation to general metric spaces. We explore how well Fr\'echet means can be estimated from independent and identically distributed samples and uncover a fundamental…
In the approximate integration some inequalities between the quadratures and the integrals approximated by them are called \emph{extremalities}. On the other hand, the set of all quadratures is convex. We are trying to find possible…