Related papers: Translation Invariant Fr\'echet Distance Queries
Let $P$ be a polygonal curve in $\mathbb{R}^d$ of length $n$, and $S$ be a point-set of size $k$. The Curve/Point Set Matching problem consists of finding a polygonal curve $Q$ on $S$ such that the Fr\'echet distance from $P$ is less than a…
We study approximating the continuous Fr\'echet distance of two curves with complexity $n$ and $m$, under the assumption that only one of the two curves is $c$-packed. Driemel, Har{-}Peled and Wenk DCG'12 studied Fr\'echet distance…
Merge trees are a common topological descriptor for data with a hierarchical component, such as terrains and scalar fields. The interleaving distance, in turn, is a common distance for comparing merge trees. However, the interleaving…
Given two sets of points A and B, $|A| = m$, $|B| = n$, the Chamfer distance from $A$ to $B$ is defined as $\operatorname{CD}(A,B) = \sum_{a\in A} \min_{b\in B} d(a,b)$, where $d$ is a distance metric. Chamfer distance is a popular measure…
Optimal transport (OT) is a popular tool in machine learning to compare probability measures geometrically, but it comes with substantial computational burden. Linear programming algorithms for computing OT distances scale cubically in the…
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…
Given two polygonal curves, there are many ways to define a notion of similarity between them. One popular measure is the Fr\'echet distance which has many desirable properties but is notoriously expensive to calculate, especially for…
We study the problem of computing the upper bound of the discrete Fr\'{e}chet distance for imprecise input, and prove that the problem is NP-hard. This solves an open problem posed in 2010 by Ahn \emph{et al}. If shortcuts are allowed, we…
We present simple and practical $(1+\eps)$-approximation algorithm for the Frechet distance between curves. To analyze this algorithm we introduce a new realistic family of curves, $c$-packed curves, that is closed under simplification. We…
Due to its many applications, \emph{curve simplification} is a long-studied problem in computational geometry and adjacent disciplines, such as graphics, geographical information science, etc. Given a polygonal curve $P$ with $n$ vertices,…
Graph comparison deals with identifying similarities and dissimilarities between graphs. A major obstacle is the unknown alignment of graphs, as well as the lack of accurate and inexpensive comparison metrics. In this work we introduce the…
Modern tracking technology has made the collection of large numbers of densely sampled trajectories of moving objects widely available. We consider a fundamental problem encountered when analysing such data: Given $n$ polygonal curves $S$…
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…
Imagine you are a dog behind a fence $Q$ and a hiker is passing by at constant speed along the hiking path $P$. In order to fulfil your duties as a watchdog, you desire to bark as long as possible at the human. However, your barks can only…
Optimal transport distances have become a classic tool to compare probability distributions and have found many applications in machine learning. Yet, despite recent algorithmic developments, their complexity prevents their direct use on…
Subtrajectory clustering is an important variant of the trajectory clustering problem, where the start and endpoints of trajectory patterns within the collected trajectory data are not known in advance. We study this problem in the form of…
We study edit distance computation with preprocessing: the preprocessing algorithm acts on each string separately, and then the query algorithm takes as input the two preprocessed strings. This model is inspired by scenarios where we would…
Similar subtrajectory search is a finer-grained operator that can better capture the similarities between one query trajectory and a portion of a data trajectory than the traditional similar trajectory search, which requires the two checked…
We study approximate-near-neighbor data structures for time series under the continuous Fr\'echet distance. For an attainable approximation factor $c>1$ and a query radius $r$, an approximate-near-neighbor data structure can be used to…
Ordered search is the task of finding an item in an ordered list using comparison queries. The best exact classical algorithm for this fundamental problem uses $\lceil \log_{2}{n}\rceil$ queries for a list of length $n$. Quantum computers…