Related papers: Fr\'echet Distance Problems in Weighted Regions
The Fr\'echet distance is a popular similarity measure that is well-understood for polygonal curves in $\mathbb{R}^d$: near-quadratic time algorithms exist, and conditional lower bounds suggest that these results cannot be improved…
Computing the Fr\'{e}chet distance for surfaces is a surprisingly hard problem and the only known algorithm is limited to computing it between flat surfaces. We adapt this algorithm to create one for computing the Fr\'{e}chet distance for a…
Given two simplicial complexes in R^d, and start and end vertices in each complex, we show how to compute curves (in each complex) between these vertices, such that the Fr\'echet distance between these curves is minimized. As a polygonal…
The similarity of two polygonal curves can be measured using the Fr\'echet distance. We introduce the notion of a more robust Fr\'echet distance, where one is allowed to shortcut between vertices of one of the curves. This is a natural…
The Fr\'echet distance is a distance measure between trajectories in $\Bbb{R}^d$ or walks in a graph $G$. Given constant-time shortest path queries, the Discrete Fr\'echet distance $D_G(P, Q)$ between two walks $P$ and $Q$ can be computed…
Computing the Fr\'echet distance between two polygonal curves takes roughly quadratic time. In this paper, we show that for a special class of curves the Fr\'echet distance computations become easier. Let $P$ and $Q$ be two polygonal curves…
We study the shortcut Fr\'{e}chet distance, a natural variant of the Fr\'{e}chet distance, that allows us to take shortcuts from and to any point along one of the curves. The classic Fr\'echet distance is a bottle-neck distance measure and…
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 consider the problem of computing the Fr\'echet distance between two curves for which the exact locations of the vertices are unknown. Each vertex may be placed in a given uncertainty region for that vertex, and the objective is to place…
A suitable measure for the similarity of shapes represented by parameterized curves or surfaces is the Fr\'echet distance. Whereas efficient algorithms are known for computing the Fr\'echet distance of polygonal curves, the same problem for…
Given two polygonal curves $P$ and $Q$ defined by $n$ and $m$ vertices with $m\leq n$, we show that the discrete Fr\'echet distance in 1D cannot be approximated within a factor of $2-\varepsilon$ in $\mathcal{O}((nm)^{1-\delta})$ time for…
The Fr\'echet distance is a computational mainstay for comparing polygonal curves. The Fr\'echet distance under translation, which is a translation invariant version, considers the similarity of two curves independent of their location in…
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 measure of dissimilarity for polygonal curves. It is defined as a min-max formulation that considers all direction-preserving continuous bijections of the two curves. Because of its susceptibility to…
The Fr\'echet distance is a popular distance measure between trajectories or curves in space, or between walks in graphs. We study computing the Fr\'echet distance between walks in the $d$-dimensional grid graphs, i.e. $\mathbb{Z}^d$ where…
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…
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This paper presents an approximation algorithm for finding a shortest path between two points $s$ and $t$ in a weighted planar subdivision $\PS$. Each face $f$ of $\PS$ is associated with a weight $w_f$, and the cost of travel along a line…
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…
The Fr\'echet distance is a popular similarity measure between curves. For some applications, it is desirable to match the curves under translation before computing the Fr\'echet distance between them. This variant is called the Translation…