S. Steinerberger

activity

20152022

most citedStochastic Neighbor Embedding separates well-separated clusters

15 citations · 45 across the 31 of their papers we have counts for

collaborators

Showing math.COShow all

7 papers · 1 filter

math.CO2022

Sums of Distances on Graphs and Embeddings into Euclidean Space

Stefan Steinerberger

Let $G = (V, E)$ be a finite, connected graph. We consider a greedy selection of vertices: given a list of vertices $x_{1}, \dots, x_{k}$ , take $x_{k + 1}$ to be any vertex maximizing the s…

math.CO2022

The Boundary of a Graph and its Isoperimetric Inequality

Stefan Steinerberger

We define, for any graph $G = (V, E)$ , a boundary $\partial G \subseteq V$ . The definition coincides with what one would expected for the discretization of (sufficiently nice) Euclide…

math.CO2021

A Graph Decomposition motivated by the Geometry of Randomized Rounding

Stefan Steinerberger

We introduce a graph decomposition which exists for all simple, connected graphs $G = (V, E)$ . The decomposition $V = A \cup B \cup C$ is such that each vertex in $A$ has more neighbo…

math.CO2020

A Spectral Approach to the Shortest Path Problem

Stefan Steinerberger

Let $G = (V, E)$ be a simple, connected graph. One is often interested in a short path between two vertices $u, v$ . We propose a spectral algorithm: construct the function $ϕ:V \righta…

math.CO2019

Dynamically Defined Sequences with Small Discrepancy

Stefan Steinerberger

We study the problem of constructing sequences $(x_{n})_{n = 1}^{\infty}$ on $[0, 1]$ in such a way that $$ D_N^* = \sup_{0 \leq x \leq 1} \left| \frac{ \left\{1 \leq i \leq N: x_i \leq…

math.CO2018

Generalized Designs on Graphs: Sampling, Spectra, Symmetries

Stefan Steinerberger

Spherical Designs are finite sets of points on the sphere $S^{d}$ with the property that the average of certain (low-degree) polynomials in these points coincides with the…