Publications related to Minimal graphs for 2-factor extension

Moments of the number of points in a bounded set for number field lattices

Maryna Viazovska, Vlad Serban, Nihar Prakash Gargava

We examine the moments of the number of lattice points in a fixed ball of volume

V

for lattices in Euclidean space which are modules over the ring of integers of a number field

K

. In particular, denoting by

ω_K

the number of roots of unity in

K

, we ...

arXiv2023

Scalable maximal subgraph mining with backbone-preserving graph convolutions

Karl Aberer, Thanh Trung Huynh, Quoc Viet Hung Nguyen, Thành Tâm Nguyên

Maximal subgraph mining is increasingly important in various domains, including bioinformatics, genomics, and chemistry, as it helps identify common characteristics among a set of graphs and enables their classification into different categories. Existing ...

ELSEVIER SCIENCE INC2023

Random walks and forbidden minors III: poly(d epsilon(-1))-time partition oracles for minor-free graph classes

Akash Kumar

Consider the family of bounded degree graphs in any minor-closed family (such as planar graphs). Let d be the degree bound and n be the number of vertices of such a graph. Graphs in these classes have hyperfinite decompositions, where, one removes a small ...

IEEE COMPUTER SOC2022

SPECTRE: Spectral Conditioning Helps to Overcome the Expressivity Limits of One-shot Graph Generators

Nathanaël Perraudin, Andreas Loukas, Karolis Martinkus

We approach the graph generation problem from a spectral perspective by first generating the dominant parts of the graph Laplacian spectrum and then building a graph matching these eigenvalues and eigenvectors. Spectral conditioning allows for direct model ...

JMLR-JOURNAL MACHINE LEARNING RESEARCH2022

Nature vs. Nurture: Feature vs. Structure for Graph Neural Networks

Karl Aberer, Thành Tâm Nguyên, Chi Thang Duong

Graph neural networks take node features and graph structure as input to build representations for nodes and graphs. While there are a lot of focus on GNN models, understanding the impact of node features and graph structure to GNN performance has received ...

ELSEVIER2022

Space-Efficient Representations of Graphs

Jakab Tardos

With the increasing prevalence of massive datasets, it becomes important to design algorithmic techniques for dealing with scenarios where the input to be processed does not fit in the memory of a single machine. Many highly successful approaches have emer ...

EPFL2022

A Unified Experiment Design Approach for Cyclic and Acyclic Causal Models

Negar Kiyavash, Ehsan Mokhtarian, Saber Salehkaleybar

We study experiment design for unique identification of the causal graph of a system where the graph may contain cycles. The presence of cycles in the structure introduces major challenges for experiment design as, unlike acyclic graphs, learning the skele ...

2022

Planted matching problems on random hypergraphs

Lenka Zdeborová, Anshul Toshniwal, Gabriele Sicuro

We consider the problem of inferring a matching hidden in a weighted random k-hypergraph. We assume that the hyperedges' weights are random and distributed according to two different densities conditioning on the fact that they belong to the hidden matchin ...

2022

On the robustness of the metric dimension of grid graphs to adding a single edge

Patrick Thiran, Gergely Odor, Satvik Mehul Mashkaria

The metric dimension (MD) of a graph is a combinatorial notion capturing the minimum number of landmark nodes needed to distinguish every pair of nodes in the graph based on graph distance. We study how much the MD can increase if we add a single edge to t ...

2022

Fourier non-uniqueness sets from totally real number fields

Martin Peter Stoller

Let K be a totally real number field of degree n >= 2. The inverse different of K gives rise to a lattice in Rn. We prove that the space of Schwartz Fourier eigenfunctions on R-n which vanish on the "component-wise square root" of this lattice, is infinite ...

EUROPEAN MATHEMATICAL SOC-EMS2022

Minimal graphs for 2-factor extension

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Moments of the number of points in a bounded set for number field lattices

Scalable maximal subgraph mining with backbone-preserving graph convolutions

Random walks and forbidden minors III: poly(d epsilon(-1))-time partition oracles for minor-free graph classes

SPECTRE: Spectral Conditioning Helps to Overcome the Expressivity Limits of One-shot Graph Generators

Nature vs. Nurture: Feature vs. Structure for Graph Neural Networks

Space-Efficient Representations of Graphs

A Unified Experiment Design Approach for Cyclic and Acyclic Causal Models

Planted matching problems on random hypergraphs

On the robustness of the metric dimension of grid graphs to adding a single edge

Fourier non-uniqueness sets from totally real number fields

Moments of the number of points in a bounded set for number field lattices

Random walks and forbidden minors III: poly(d epsilon(-1))-time partition oracles for minor-free graph classes

Scalable maximal subgraph mining with backbone-preserving graph convolutions

Fourier non-uniqueness sets from totally real number fields

SPECTRE: Spectral Conditioning Helps to Overcome the Expressivity Limits of One-shot Graph Generators

Nature vs. Nurture: Feature vs. Structure for Graph Neural Networks

Space-Efficient Representations of Graphs

A Unified Experiment Design Approach for Cyclic and Acyclic Causal Models

Planted matching problems on random hypergraphs

On the robustness of the metric dimension of grid graphs to adding a single edge