Related papers: Fr\'echet Distance in Subquadratic Time
The Fr\'echet distance provides a natural and intuitive measure for the popular task of computing the similarity of two (polygonal) curves. While a simple algorithm computes it in near-quadratic time, a strongly subquadratic algorithm…
We discuss two versions of the Fr\'echet distance problem in weighted planar subdivisions. In the first one, the distance between two points is the weighted length of the line segment joining the points. In the second one, the distance…
We describe a $O(\log n )$-approximation algorithm for computing the homotopic \Frechet distance between two polygonal curves that lie on the boundary of a triangulated topological disk. Prior to this work, algorithms were known only for…
The Frechet distance is a metric to compare two curves, which is based on monotonous matchings between these curves. We call a matching that results in the Frechet distance a Frechet matching. There are often many different Frechet…
We give algorithms to compute the Fr\'echet distance of trees and graphs with bounded tree width. Our algorithms run in $O(n^2)$ time for trees of bounded degree, and $O(n^2\sqrt{n \log n})$ time for trees of arbitrary degree. For graphs of…
Consider the natural question of how to measure the similarity of curves in the plane by a quantity that is invariant under translations of the curves. Such a measure is justified whenever we aim to quantify the similarity of the curves'…
The Fr\'{e}chet distance is a well studied and commonly used measure to capture the similarity of polygonal curves. Unfortunately, it exhibits a high sensitivity to the presence of outliers. Since the presence of outliers is a frequently…
The discrete Fr\'echet distance is a useful similarity measure for comparing two sequences of points $P=(p_1,\ldots, p_m)$ and $Q=(q_1,\ldots,q_n)$. In many applications, the quality of the matching can be improved if we let $Q$ undergo…
One approach to studying the Fr\'echet distance is to consider curves that satisfy realistic assumptions. By now, the most popular realistic assumption for curves is $c$-packedness. Existing algorithms for computing the Fr\'echet distance…
We show by reduction from the Orthogonal Vectors problem that algorithms with strongly subquadratic running time cannot approximate the Fr\'echet distance between curves better than a factor $3$ unless SETH fails. We show that similar…
We introduce a new distance measure for comparing polygonal chains: the $k$-Fr\'echet distance. As the name implies, it is closely related to the well-studied Fr\'echet distance but detects similarities between curves that resemble each…
The Fr\'echet distance is a popular distance measure for curves. We study the problem of clustering time series under the Fr\'echet distance. In particular, we give $(1+\varepsilon)$-approximation algorithms for variations of the following…
The Fr\'echet distance is a popular metric for curves; however, its bottleneck character is a disadvantage in many applications. Here we introduce two variants of the Fr\'echet distance to cope with this problem and expand the work on…
We study data structures for storing a set of polygonal curves in ${\rm R}^d$ such that, given a query curve, we can efficiently retrieve similar curves from the set, where similarity is measured using the discrete Fr\'echet distance or the…
We define and investigate the Fr\'{e}chet edit distance problem. Given two polygonal curves $\pi$ and $\sigma$ and a threshhold value $\delta>0$, we seek the minimum number of edits to $\sigma$ such that the Fr\'{e}chet distance between the…
We unveil an alluring alternative to parametric search that applies to both the non-geodesic and geodesic Fr\'echet optimization problems. This randomized approach is based on a variant of red-blue intersections and is appealing due to its…
In this paper we study a wide range of variants for computing the (discrete and continuous) Fr\'echet distance between uncertain curves. We define an uncertain curve as a sequence of uncertainty regions, where each region is a disk, a line…
We show that a variant of the continuous Frechet distance between polygonal curves can be computed using essentially the same algorithm used to solve the discrete version. The new variant is not necessarily monotone, but this shortcoming…
The Fr\'echet distance is a popular distance measure for curves which naturally lends itself to fundamental computational tasks, such as clustering, nearest-neighbor searching, and spherical range searching in the corresponding metric…
A pseudo-polynomial time $(1 + \varepsilon)$-approximation algorithm is presented for computing the integral and average Fr\'{e}chet distance between two given polygonal curves $T_1$ and $T_2$. In particular, the running time is…