Related papers: Barking dogs: A Fr\'echet distance variant for det…
Performing random walks in networks is a fundamental primitive that has found applications in many areas of computer science, including distributed computing. In this paper, we focus on the problem of sampling random walks efficiently in a…
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…
Tree comparison metrics have proven to be an invaluable aide in the reconstruction and analysis of phylogenetic (evolutionary) trees. The path-length distance between trees is a particularly attractive measure as it reflects differences in…
Map matching is a common task when analysing GPS tracks, such as vehicle trajectories. The goal is to match a recorded noisy polygonal curve to a path on the map, usually represented as a geometric graph. The Fr\'echet distance is a…
We consider a random walk in a fixed Z environment composed of two point types: (q,1-q) and (p,1-p) for 1/2<q<p. We study the expected hitting time at N for a given number k of p-drifts in the interval [1,N-1], and find that this time is…
The Dynamic Time Warping (DTW) distance is a popular measure of similarity for a variety of sequence data. For comparing polygonal curves $\pi, \sigma$ in $\mathbb{R}^d$, it provides a robust, outlier-insensitive alternative to the…
Computing the similarity between two data points plays a vital role in many machine learning algorithms. Metric learning has the aim of learning a good metric automatically from data. Most existing studies on metric learning for…
Optimal transport provides a metric which quantifies the dissimilarity between probability measures. For measures supported in discrete metric spaces, finding the optimal transport distance has cubic time complexity in the size of the…
The problem of finding \emph{distance} between \emph{pattern} of length $m$ and \emph{text} of length $n$ is a typical way of generalizing pattern matching to incorporate dissimilarity score. For both Hamming and $L_1$ distances only a…
Patrolling consists of scheduling perpetual movements of a collection of mobile robots, so that each point of the environment is regularly revisited by any robot in the collection. In previous research, it was assumed that all points of the…
Most existing distance metric learning methods assume perfect side information that is usually given in pairwise or triplet constraints. Instead, in many real-world applications, the constraints are derived from side information, such as…
A set of piecewise linear functions, called polylines, $P_1,\ldots,P_L$ each with at most $n$ vertices can be simplified into a polyline $M$ with $k$ vertices, such that the Fr\'echet distances $\epsilon_1,\ldots,\epsilon_L$ to each of…
In this paper, we consider the problem of protecting a high-value unit from inadvertent attack by a group of agents using defending robots. Specifically, we develop a control strategy for the defending agents that we call "dog robots" to…
We revisit the classical polygonal line simplification problem and study it using the Hausdorff distance and Fr\'echet distance. Interestingly, no previous authors studied line simplification under these measures in its pure form, namely:…
The \emph{Skorokhod distance} is a natural metric on traces of continuous and hybrid systems. For two traces, from $[0,T]$ to values in a metric space $O$, it measures the best match between the traces when allowed continuous bijective…
This paper describes an implementation of fast near-neighbours queries (also known as range searching) with respect to the Fr\'echet distance. The algorithm is designed to be efficient on practical data such as GPS trajectories. Our…
Given a geometric domain $P$, visibility-based search problems seek routes for one or more mobile agents ("watchmen") to move within $P$ in order to be able to see a portion (or all) of $P$, while optimizing objectives, such as the…
In this paper, we propose new techniques for solving geometric optimization problems involving interpoint distances of a point set in the plane. Given a set $P$ of $n$ points in the plane and an integer $1 \leq k \leq \binom{n}{2}$, the…
We consider a perimeter defense problem in a planar conical environment comprising a single turret that has a finite range and non-zero service time. The turret seeks to defend a concentric perimeter against $N\geq 2$ intruders. Upon…
The study of animal movement is challenging because it is a process modulated by many factors acting at different spatial and temporal scales. Several models have been proposed which differ primarily in the temporal conceptualization,…