Search Results for author: Benjamin Raichel

Found 6 papers, 0 papers with code

On Cyclic Solutions to the Min-Max Latency Multi-Robot Patrolling Problem

no code implementations14 Mar 2022 Peyman Afshani, Mark De Berg, Kevin Buchin, Jie Gao, Maarten Loffler, Amir Nayyeri, Benjamin Raichel, Rik Sarkar, Haotian Wang, Hao-Tsung Yang

For the Euclidean version of the problem, for instance, combining our results with known results on Euclidean TSP, yields a PTAS for approximating an optimal cyclic solution, and it yields a $(2(1-1/k)+\varepsilon)$-approximation of the optimal unrestricted solution.

How can classical multidimensional scaling go wrong?

no code implementations NeurIPS 2021 Rishi Sonthalia, Gregory Van Buskirk, Benjamin Raichel, Anna C. Gilbert

While $D_l$ is not metric, when given as input to cMDS instead of $D$, it empirically results in solutions whose distance to $D$ does not increase when we increase the dimension and the classification accuracy degrades less than the cMDS solution.

Fréchet Distance for Uncertain Curves

no code implementations24 Apr 2020 Kevin Buchin, Chenglin Fan, Maarten Löffler, Aleksandr Popov, Benjamin Raichel, Marcel Roeloffzen

We prove that both the upper and lower bound problems are NP-hard for the continuous Fr\'echet distance in several uncertainty models, and that the upper bound problem remains hard for the discrete Fr\'echet distance.

Computational Geometry

Sparse Approximate Conic Hulls

no code implementations NeurIPS 2017 Greg Van Buskirk, Benjamin Raichel, Nicholas Ruozzi

Equivalently, given the matrix X, consider the problem of finding a small subset, S, of the columns of X such that the conic hull of S \eps-approximates the conic hull of the columns of X, i. e., the distance of every column of X to the conic hull of the columns of S should be at most an \eps-fraction of the angular diameter of X.

Sparse Approximation via Generating Point Sets

no code implementations9 Jul 2015 Avrim Blum, Sariel Har-Peled, Benjamin Raichel

]{#1\left({#2}\right)} \newcommand{\npoints}{n} \newcommand{\ballD}{\mathsf{b}} \newcommand{\dataset}{{P}} $ For a set $\dataset$ of $\npoints$ points in the unit ball $\ballD \subseteq \Re^d$, consider the problem of finding a small subset $\algset \subseteq \dataset$ such that its convex-hull $\eps$-approximates the convex-hull of the original set.

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