English
Related papers

Related papers: Map-Matching Queries under Fr\'echet Distance on L…

200 papers

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…

Computational Geometry · Computer Science 2010-04-29 Yam Ki Cheung , Ovidiu Daescu

In this paper, we study the problem of map matching with travel time constraints. Given a sequence of $k$ spatio-temporal measurements and an embedded path graph with travel time costs, the goal is to snap each measurement to a close-by…

Computational Geometry · Computer Science 2025-06-24 Yannick Bosch , Sabine Storandt

We study the problem of sub-trajectory nearest-neighbor queries on polygonal curves under the continuous Fr\'echet distance. Given an $n$ vertex trajectory $P$ and an $m$ vertex query trajectory $Q$, we seek to report a vertex-aligned…

Computational Geometry · Computer Science 2024-01-17 Joachim Gudmundsson , John Pfeifer , Martin P. Seybold

We introduce the discrete Fr\'echet gap and its variants as an alternative measure of similarity between polygonal curves. We believe that for some applications the new measure (and its variants) may better reflect our intuitive notion of…

Computational Geometry · Computer Science 2015-06-17 Omrit Filtser , Matthew J. Katz

The \emph{Fr\'echet distance} is a well studied similarity measures between curves. The \emph{discrete Fr\'echet distance} is an analogous similarity measure, defined for a sequence $A$ of $m$ points and a sequence $B$ of $n$ points, where…

Computational Geometry · Computer Science 2016-09-09 Rinat Ben Avraham , Omrit Filtser , Haim Kaplan , Matthew J. Katz , Micha Sharir

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…

Computational Geometry · Computer Science 2025-01-23 Lotte Blank , Jacobus Conradi , Anne Driemel , Benedikt Kolbe , André Nusser , Marena Richter

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…

Computational Geometry · Computer Science 2021-08-13 Joachim Gudmundsson , André van Renssen , Zeinab Saeidi , Sampson Wong

We propose sublinear algorithms for probabilistic testing of the discrete and continuous Fr\'echet distance - a standard similarity measure for curves. We assume the algorithm is given access to the input curves via a query oracle: a query…

Computational Geometry · Computer Science 2025-09-05 Peyman Afshani , Maike Buchin , Anne Driemel , Marena Richter , Sampson Wong

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…

Computational Geometry · Computer Science 2026-01-01 Sariel Har-Peled , Benjamin Raichel , Eliot W. Robson

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…

Computational Geometry · Computer Science 2012-06-28 Kevin Buchin , Maike Buchin , Wouter Meulemans , Bettina Speckmann

The discrete Fr\'echet distance is a popular measure for comparing polygonal curves. An important variant is the discrete Fr\'echet distance under translation, which enables detection of similar movement patterns in different spatial…

Data Structures and Algorithms · Computer Science 2021-10-13 Karl Bringmann , Marvin Künnemann , André Nusser

We present an anytime algorithm that generates a collision-free configuration-space path that closely follows a desired path in task space, according to the discrete Frechet distance. By leveraging tools from computational geometry, we…

Robotics · Computer Science 2021-01-01 Rachel Holladay , Oren Salzman , Siddhartha Srinivasa

The growing use of probe vehicles generates a huge number of GNSS data. Limited by the satellite positioning technology, further improving the accuracy of map-matching is challenging work, especially for low-frequency trajectories. When…

Systems and Control · Electrical Eng. & Systems 2022-09-20 Jie Fang , Xiongwei Wu , Dianchao Lin , Mengyun Xu , Huahua Wu , Xuesong Wu , Ting Bi

Comparison of graph structure is a ubiquitous task in data analysis and machine learning, with diverse applications in fields such as neuroscience, cyber security, social network analysis, and bioinformatics, among others. Discovery and…

Applications · Statistics 2023-01-11 Peter Wills , Francois G. Meyer

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'…

Computational Geometry · Computer Science 2020-08-18 Karl Bringmann , Marvin Künnemann , André Nusser

In 2012 Driemel et al. \cite{DBLP:journals/dcg/DriemelHW12} introduced the concept of $c$-packed curves as a realistic input model. In the case when $c$ is a constant they gave a near linear time $(1+\varepsilon)$-approximation algorithm…

Computational Geometry · Computer Science 2020-09-18 Joachim Gudmundsson , Yuan Sha , Sampson Wong

The computation of distance measures between nodes in graphs is inefficient and does not scale to large graphs. We explore dense vector representations as an effective way to approximate the same information: we introduce a simple yet…

Computation and Language · Computer Science 2019-06-18 Andrey Kutuzov , Mohammad Dorgham , Oleksiy Oliynyk , Chris Biemann , Alexander Panchenko

We introduce new distance measures for comparing straight-line embedded graphs based on the Fr\'echet distance and the weak Fr\'echet distance. These graph distances are defined using continuous mappings and thus take the combinatorial…

Computational Geometry · Computer Science 2019-09-12 Hugo A. Akitaya , Maike Buchin , Bernhard Kilgus , Stef Sijben , Carola Wenk

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 its Fr\'echet distance from $P$ is less than a…

Computational Geometry · Computer Science 2014-05-06 Paul Accisano , Alper Üngör

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…

Computational Geometry · Computer Science 2019-03-07 Hugo A Akitaya , Maike Buchin , Leonie Ryvkin , Jérôme Urhausen