Patrick Schnider

activity

20242026

collaborators

16 papers

cs.CG2026

The Inverse Mapper Problem for Two-Dimensional Data

Robin Belton, Patrick Schnider

The Mapper algorithm is a popular graphical tool for data visualization and exploration in topological data analysis (TDA). It takes as input a data set $X$ and returns a graph tha…

cs.CG2026

Bowties and Hourglasses: Intersections of Double-Wedges (or Stabbing and Avoiding Line Segments)

Daniel Bertschinger, Henry Förster, Fabian Klute +3

We study the common intersection of arrangements of double-wedges. We consider arrangements where double-wedges may be either bowties (which do not contain a vertical line) or hour…

cs.CG2026

Garment numbers of bi-colored point sets in the plane

Oswin Aichholzer, Helena Bergold, Simon D. Fink +3

We consider colored variants of a class of geometric-combinatorial questions on $k$ -gons and empty $k$ -gons that have been started around 1935 by Erdős and Szekeres. In our setting…

math.CO2026

Splitting Sandwiches Unevenly via Unique Sink Orientations and Rainbow Arrangements

Michaela Borzechowski, Sebastian Haslebacher, Hung P. Hoang +2

The famous Ham-Sandwich theorem states that any $d$ point sets in $R^{d}$ can be simultaneously bisected by a single hyperplane. The $α$ -Ham-Sandwich theorem gives a suffici…

cs.LG2025

LEAP: Local ECT-Based Learnable Positional Encodings for Graphs

Juan Amboage, Ernst Röell, Patrick Schnider +1

Graph neural networks (GNNs) largely rely on the message-passing paradigm, where nodes iteratively aggregate information from their neighbors. Yet, standard message passing neural…

math.AT2025

Flagifying the Dowker Complex

Marius Huber, Patrick Schnider

The Dowker complex $D_{R} (X, Y)$ is a simplicial complex capturing the topological interplay between two finite sets $X$ and $Y$ under some relation $R \subseteq X \times Y$ .…

cs.CC2025

Query-Efficient Fixpoints of $ℓ_{p}$ -Contractions

Sebastian Haslebacher, Jonas Lill, Patrick Schnider +1

We prove that an $ε$ -approximate fixpoint of a map $f : [0, 1]^{d} \to [0, 1]^{d}$ can be found with $O (d^{2} (lo g \frac{1}{ε} + lo g \frac{1}{1 - λ}))$ queries to $f$ if $f$ is $…

cs.CG2025

Chasing puppies on orthogonal straight-line plane graphs

Johanna Ockenfels, Yoshio Okamoto, Patrick Schnider

Assume that you have lost your puppy on an embedded graph. You can walk around on the graph and the puppy will run towards you at infinite speed, always locally minimizing the dist…

cs.CG2025

Bounds for k-centers of point sets under $L_{\infty}$ -bottleneck distance

Mats Bierwirth, Julia Hütte, Patrick Schnider +1

We consider the $k$ -center problem on the space of fixed-size point sets in the plane under the $L_{\infty}$ -bottleneck distance. While this problem is motivated by persistence dia…

cs.CG2024

Flips in Odd Matchings

Oswin Aichholzer, Anna Brötzner, Daniel Perz +1

Let $P$ be a set of $n = 2 m + 1$ points in the plane in general position. We define the graph $G M_{P}$ whose vertex set is the set of all plane matchings on $\mathcal…

cs.DS2024

Unfairly Splitting Separable Necklaces

Patrick Schnider, Linus Stalder, Simon Weber

The Necklace Splitting problem is a classical problem in combinatorics that has been intensively studied both from a combinatorial and a computational point of view. It is well-kno…

cs.LG2024

AuToMATo: An Out-Of-The-Box Persistence-Based Clustering Algorithm

Marius Huber, Sara Kalisnik, Patrick Schnider

We present AuToMATo, a novel clustering algorithm based on persistent homology. While AuToMATo is not parameter-free per se, we provide default choices for its parameters that make…

cs.CG2024

Connected Matchings

Oswin Aichholzer, Sergio Cabello, Viola Mészáros +2

We show that each set of $n \geq 2$ points in the plane in general position has a straight-line matching with at least $(5 n + 1) /27$ edges whose segments form a connected set, and such…

cs.CG2024

Barking dogs: A Fréchet distance variant for detour detection

Ivor van der Hoog, Fabian Klute, Irene Parada +1

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…

cs.CG2024

Computing Enclosing Depth

Bernd Gärtner, Fatime Rasiti, Patrick Schnider

Enclosing depth is a recently introduced depth measure which gives a lower bound to many depth measures studied in the literature. So far, enclosing depth has only been studied fro…

cs.CC2024

Two Choices are Enough for P-LCPs, USOs, and Colorful Tangents

Michaela Borzechowski, John Fearnley, Spencer Gordon +3

We provide polynomial-time reductions between three search problems from three distinct areas: the P-matrix linear complementarity problem (P-LCP), finding the sink of a unique sin…

The Inverse Mapper Problem for Two-Dimensional Data

Bowties and Hourglasses: Intersections of Double-Wedges (or Stabbing and Avoiding Line Segments)

Garment numbers of bi-colored point sets in the plane

Splitting Sandwiches Unevenly via Unique Sink Orientations and Rainbow Arrangements

LEAP: Local ECT-Based Learnable Positional Encodings for Graphs

Flagifying the Dowker Complex

Query-Efficient Fixpoints of ℓp​-Contractions

Chasing puppies on orthogonal straight-line plane graphs

Bounds for k-centers of point sets under L∞​-bottleneck distance

Flips in Odd Matchings

Unfairly Splitting Separable Necklaces

AuToMATo: An Out-Of-The-Box Persistence-Based Clustering Algorithm

Connected Matchings

Barking dogs: A Fréchet distance variant for detour detection

Computing Enclosing Depth

Two Choices are Enough for P-LCPs, USOs, and Colorful Tangents

Query-Efficient Fixpoints of $ℓ_{p}$ -Contractions

Bounds for k-centers of point sets under $L_{\infty}$ -bottleneck distance