10 citations · 25 across the 10 of their papers we have counts for
13 papers
A Topological Version of Schaefer's Dichotomy Theorem
Patrick Schnider, Simon Weber
Schaefer's dichotomy theorem [Schaefer, STOC'78] states that a boolean constraint satisfaction problem (CSP) is polynomial-time solvable if one of six given conditions holds for ev…
An FPT Algorithm for Splitting a Necklace Among Two Thieves
Michaela Borzechowski, Patrick Schnider, Simon Weber
It is well-known that the 2-Thief-Necklace-Splitting problem reduces to the discrete Ham Sandwich problem. In fact, this reduction was crucial in the proof of the PPA-completeness…
On Connectivity in Random Graph Models with Limited Dependencies
Johannes Lengler, Anders Martinsson, Kalina Petrova +4
For any positive edge density , a random graph in the Erdős-Renyi model is connected with non-zero probability, since all edges are mutually independent. We consider r…
On the Complexity of Recognizing Nerves of Convex Sets
Patrick Schnider, Simon Weber
We study the problem of recognizing whether a given abstract simplicial complex is the -skeleton of the nerve of -dimensional convex sets in . We denote thi…
Reducing Nearest Neighbor Training Sets Optimally and Exactly
Josiah Rohrer, Simon Weber
In nearest-neighbor classification, a training set of points in with given classification is used to classify every point in : Every point gets the…
On Degeneracy in the P-Matroid Oriented Matroid Complementarity Problem
Michaela Borzechowski, Simon Weber
Klaus showed that the Oriented Matroid Complementarity Problem (OMCP) can be solved by a reduction to the problem of sink-finding in a unique sink orientation (USO) if the input is…
The Complexity of Recognizing Geometric Hypergraphs
Daniel Bertschinger, Nicolas El Maalouly, Linda Kleist +2
As set systems, hypergraphs are omnipresent and have various representations ranging from Euler and Venn diagrams to contact representations. In a geometric representation of a hyp…
A Universal Construction for Unique Sink Orientations
Michaela Borzechowski, Joseph Doolittle, Simon Weber
Unique Sink Orientations (USOs) of cubes can be used to capture the combinatorial structure of many essential algebraic and geometric problems. For various structural and algorithm…
Realizability Makes a Difference: A Complexity Gap for Sink-Finding in USOs
Simon Weber, Joel Widmer
Algorithms for finding the sink in Unique Sink Orientations (USOs) of the hypercube can be used to solve many algebraic and geometric problems, most importantly including the P-Mat…
Training Fully Connected Neural Networks is -Complete
Daniel Bertschinger, Christoph Hertrich, Paul Jungeblut +2
We consider the problem of finding weights and biases for a two-layer fully connected neural network to fit a given set of data points as well as possible, also known as EmpiricalR…
A Characterization of the Realizable Matoušek Unique Sink Orientations
Simon Weber, Bernd Gärtner
The Matoušek LP-type problems were used by Matoušek to show that the Sharir-Welzl algorithm may require at least subexponential time. Later, Gärtner translated this result into the…
Topological Art in Simple Galleries
Daniel Bertschinger, Nicolas El Maalouly, Tillmann Miltzow +2
Let be a simple polygon, then the art gallery problem is looking for a minimum set of points (guards) that can see every point in . We say two points can see each…
Algorithmic Programming Language Identification
David Klein, Kyle Murray, Simon Weber
Motivated by the amount of code that goes unidentified on the web, we introduce a practical method for algorithmically identifying the programming language of source code. Our work…