Publications related to Expander graph

Metastability of the Potts Ferromagnet on Random Regular Graphs

We study the performance of Markov chains for the q-state ferromagnetic Potts model on random regular graphs. While the cases of the grid and the complete graph are by now well-understood, the case of random regular graphs has resisted a detailed analysis ...

SPRINGER2023

Beyond Spectral Gap: The Role of the Topology in Decentralized Learning

Martin Jaggi, Thijs Vogels, Hadrien Hendrikx

In data-parallel optimization of machine learning models, workers collaborate to improve their estimates of the model: more accurate gradients allow them to use larger learning rates and optimize faster. In the decentralized setting, in which workers commu ...

Microtome Publishing2023

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

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

Karl Aberer, Quoc Viet Hung Nguyen, 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

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

fGOT: Graph Distances Based on Filters and Optimal Transport

Pascal Frossard, Mireille El Gheche, Hermina Petric Maretic, Giovanni Chierchia

Graph comparison deals with identifying similarities and dissimilarities between graphs. A major obstacle is the unknown alignment of graphs, as well as the lack of accurate and inexpensive comparison metrics. In this work we introduce the filter graph dis ...

ASSOC ADVANCEMENT ARTIFICIAL INTELLIGENCE2022

Motif Cut Sparsifiers

Mikhail Kapralov, Mikhail Makarov, Jakab Tardos

A motif is a frequently occurring subgraph of a given directed or undirected graph G (Milo et al.). Motifs capture higher order organizational structure of G beyond edge relationships, and, therefore, have found wide applications such as in graph clusterin ...

IEEE COMPUTER SOC2022

Improving the Training of Compact Neural Networks for Visual Recognition

Shuxuan Guo

During the Artificial Intelligence (AI) revolution of the past decades, deep neural networks have been widely used and have achieved tremendous success in visual recognition. Unfortunately, deploying deep models is challenging because of their huge model s ...

EPFL2022

iPool--Information-Based Pooling in Hierarchical Graph Neural Networks

Pascal Frossard, Chenglin Li, Xing Gao

With the advent of data science, the analysis of network or graph data has become a very timely research problem. A variety of recent works have been proposed to generalize neural networks to graphs, either from a spectral graph theory or a spatial perspec ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2022

How to Match in Modern Computational Settings

Buddhima Ruwanmini Gamlath Gamlath Ralalage

This thesis focuses on the maximum matching problem in modern computational settings where the algorithms have to make decisions with partial information. First, we consider two stochastic models called query-commit and price-of-information where the algo ...

EPFL2021

Faster Monotone Min-Plus Product, Range Mode, and Single Source Replacement Paths

Adam Teodor Polak

One of the most basic graph problems, All-Pairs Shortest Paths (APSP) is known to be solvable in n^{3-o(1)} time, and it is widely open whether it has an O(n^{3-ε}) time algorithm for ε > 0. To better understand APSP, one often strives to obtain subcubic t ...

Schloss Dagstuhl -- Leibniz-Zentrum für Informatik2021

Sublinear Algorithms for Spectral Graph Clustering

Aidasadat Mousavifar

This thesis focuses on designing spectral tools for graph clustering in sublinear time. With the emergence of big data, many traditional polynomial time, and even linear time algorithms have become prohibitively expensive. Processing modern datasets requir ...

EPFL2021

On the constancy theorem for anisotropic energies through differential inclusions

Riccardo Tione

In this paper we study stationary graphs for functionals of geometric nature defined on currents or varifolds. The point of view we adopt is the one of differential inclusions, introduced in this context in the recent papers (De Lellis et al. in Geometric ...

2021

Methods for functional connectivity and morphometry in neonatal neuroimaging to study neurodevelopment

Serafeim Loukas

Preterm birth is a major pediatric health problem that perturbs the genetically determined program of corticogenesis of the developing brain. As a consequence, prematurity has been strongly associated with adverse long-term neurodevelopmental outcome that ...

EPFL2021

Experiments with the Markoff Surface

Matthew De Courcy-Ireland, Sandy Lee

We confirm, for the primes up to 3000, the conjecture of Bourgain-Gamburd-Sarnak and Baragar on strong approximation for the Markoff surface modulo primes. For primes congruent to 3 modulo 4, we find data suggesting that some natural graphs constructed fro ...

TAYLOR & FRANCIS INC2022

Local approximation of the Maximum Cut in regular graphs

Etienne Michel François Bamas

This paper is devoted to the distributed complexity of finding an approximation of the maximum cut (MAXCUT) in graphs. A classical algorithm consists in letting each vertex choose its side of the cut uniformly at random. This does not require any communica ...

ELSEVIER2020

Improved Ramsey-type results for comparability graphs

Istvan Tomon, Dániel József Korándi

Several discrete geometry problems are equivalent to estimating the size of the largest homogeneous sets in graphs that happen to be the union of few comparability graphs. An important observation for such results is that if G is an n-vertex graph that is ...

CAMBRIDGE UNIV PRESS2020

Graph Coarsening with Preserved Spectral Properties

Andreas Loukas

In graph coarsening, one aims to produce a coarse graph of reduced size while preserving important graph properties. However, as there is no consensus on which specific graph properties should be preserved by coarse graphs, measuring the differences betwee ...

ADDISON-WESLEY PUBL CO2020

Fast and Space Efficient Spectral Sparsification in Dynamic Streams

Mikhail Kapralov, Jakab Tardos, Navid Nouri, Aidasadat Mousavifar

In this paper, we resolve the complexity problem of spectral graph sparcification in dynamic streams up to polylogarithmic factors. Using a linear sketch we design a streaming algorithm that uses (O) over tilde (n) space, and with high probability, recover ...

ASSOC COMPUTING MACHINERY2020