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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…
Time series similarity measures are highly relevant in a wide range of emerging applications including training machine learning models, classification, and predictive modeling. Standard similarity measures for time series most often…
Nearest neighbor search under elastic distances is a key tool for time series analysis, supporting many applications. However, straightforward implementations of distances require $O(n^2)$ space and time complexities, preventing these…
We present fully dynamic approximation algorithms for the Maximum Independent Set problem on several types of geometric objects: intervals on the real line, arbitrary axis-aligned squares in the plane and axis-aligned $d$-dimensional…
Dynamic Threshold Optimization (DTO) adaptively "compresses" the decision space (DS) in a global search and optimization problem by bounding the objective function from below. This approach is different from "shrinking" DS by reducing…
In this paper we study similarity measures for moving curves which can, for example, model changing coastlines or retreating glacier termini. Points on a moving curve have two parameters, namely the position along the curve as well as time.…
A fundamental notion of distance between train and test distributions from the field of domain adaptation is discrepancy distance. While in general hard to compute, here we provide the first set of provably efficient algorithms for testing…
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…
Recently used in various machine learning contexts, the Gromov-Wasserstein distance (GW) allows for comparing distributions whose supports do not necessarily lie in the same metric space. However, this Optimal Transport (OT) distance…
To measure the similarity of documents, the Wasserstein distance is a powerful tool, but it requires a high computational cost. Recently, for fast computation of the Wasserstein distance, methods for approximating the Wasserstein distance…
In this paper, we introduce proximal gradient temporal difference learning, which provides a principled way of designing and analyzing true stochastic gradient temporal difference learning algorithms. We show how gradient TD (GTD)…
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…
Low-cost mobile rovers often operate on uneven terrain where small bumps or tilts are difficult to perceive visually but can significantly affect locomotion stability. To address this problem, we explore a smartphone-based structured-light…
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…
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…
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This paper addresses the problem of finding a B-term wavelet representation of a given discrete function $f \in \real^n$ whose distance from f is minimized. The problem is well understood when we seek to minimize the Euclidean distance…
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…
In recent years, neural networks achieved much success in various applications. The main challenge in training deep neural networks is the lack of sufficient data to improve the model's generalization and avoid overfitting. One of the…
In many robotics applications, it is necessary to compute not only the distance between the robot and the environment, but also its derivative - for example, when using control barrier functions. However, since the traditional Euclidean…