Publications related to Many disjoint edges in topological graphs

The connection of the acyclic disconnection and feedback arc sets - On an open problem of Figueroa et al

We examine the connection of two graph parameters, the size of a minimum feedback arcs set and the acyclic disconnection. A feedback arc set of a directed graph is a subset of arcs such that after deletion the graph becomes acyclic. The acyclic disconnecti ...

Elsevier2024

Non-planarity of Markoff graphs mod p

Matthew De Courcy-Ireland

We prove the non-planarity of a family of 3-regular graphs constructed from the solutions to the Markoff equation x2 + y2 + z2 = xyz modulo prime numbers greater than 7. The proof uses Euler characteristic and an enumeration of the short cycles in these gr ...

European Mathematical Soc-Ems2024

A Note on Lenses in Arrangements of Pairwise Intersecting Circles in the Plane

Rom Pinchasi

Let F be a family of n pairwise intersecting circles in the plane. We show that the number of lenses, that is convex digons, in the arrangement induced by F is at most 2n - 2. This bound is tight. Furthermore, if no two circles in F touch, then the geometr ...

Electronic Journal Of Combinatorics2024

The Power of Two Matrices in Spectral Algorithms for Community Recovery

Colin Peter Sandon

Spectral algorithms are some of the main tools in optimization and inference problems on graphs. Typically, the graph is encoded as a matrix and eigenvectors and eigenvalues of the matrix are then used to solve the given graph problem. Spectral algorithms ...

Ieee-Inst Electrical Electronics Engineers Inc2024

GRAMM: Fast CGRA Application Mapping Based on A Heuristic for Finding Graph Minors

Mirjana Stojilovic, Guanglei Zhou

A graph H is a minor of a second graph G if G can be transformed into H by two operations: 1) deleting nodes and/or edges, or 2) contracting edges. Coarse-grained reconfigurable array (CGRA) application mapping is closely related to the graph minor problem ...

Los Alamitos2023

Better Trees for Santa Claus

Etienne Michel François Bamas, Lars Rohwedder

We revisit the problem max-min degree arborescence, which was introduced by Bateni et al. [STOC'09] as a central special case of the general Santa Claus problem, which constitutes a notorious open question in approximation algorithms. In the former problem ...

Assoc Computing Machinery2023

GAP: Differentially Private Graph Neural Networks with Aggregation Perturbation

Daniel Gatica-Perez, Sina Sajadmanesh

In this paper, we study the problem of learning Graph Neural Networks (GNNs) with Differential Privacy (DP). We propose a novel differentially private GNN based on Aggregation Perturbation (GAP), which adds stochastic noise to the GNN's aggregation functio ...

Usenix Assoc2023

Unsupervised Graph Representation Learning with Cluster-aware Self-training and Refining

Qiang Liu, Feng Yu, Yichen Xu

Unsupervised graph representation learning aims to learn low-dimensional node embeddings without supervision while preserving graph topological structures and node attributive features. Previous Graph Neural Networks (GNN) require a large number of labeled ...

Assoc Computing Machinery2023

Graph-based approximate message passing iterations

Raphaël Jean Berthier

Approximate message passing (AMP) algorithms have become an important element of high-dimensional statistical inference, mostly due to their adaptability and concentration properties, the state evolution (SE) equations. This is demonstrated by the growing ...

OXFORD UNIV PRESS2023

Results on Sparse Integer Programming and Geometric Independent Sets

Jana Tabea Cslovjecsek

An integer linear program is a problem of the form max{c^T x : Ax=b, x >= 0, x integer}, where A is in Z^(n x m), b in Z^m, and c in Z^n. Solving an integer linear program is NP-hard in general, but there are several assumptions for which it becomes fixed ...

EPFL2023

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

Thijs Vogels, Hadrien Hendrikx, Martin Jaggi

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

Equivariant Neural Architectures for Representing and Generating Graphs

Clément Arthur Yvon Vignac

Graph machine learning offers a powerful framework with natural applications in scientific fields such as chemistry, biology and material sciences. By representing data as a graph, we encode the prior knowledge that the data is composed of a set of entiti ...

EPFL2023

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

A Unified Experiment Design Approach for Cyclic and Acyclic Causal Models

Saber Salehkaleybar, Negar Kiyavash, Ehsan Mokhtarian

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 ...

2023

Graph signal processing tailored for subgraph focus and community structure

Miljan Petrovic

Community structure in graph-modeled data appears in a range of disciplines that comprise network science. Its importance relies on the influence it bears on other properties of graphs such as resilience, or prediction of missing connections. Nevertheless, ...

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

Graph Embedding for Retrieval

Chi Thang Duong

Information retrieval (IR) systems such as search engines are important for people to find what they need among the tremendous amount of data available in their organization or on the Internet. These IR systems enable users to search in a large data collec ...

EPFL2022

Graph Representation Learning with Optimal Transport: Analysis and Applications

Effrosyni Simou

In several machine learning settings, the data of interest are well described by graphs. Examples include data pertaining to transportation networks or social networks. Further, biological data, such as proteins or molecules, lend themselves well to graph- ...

EPFL2022

Toward Mobile Distributed Ledgers

Boi Faltings, Sujit Prakash Gujar, Dimitrios Chatzopoulos, Anurag Jain

Advances in mobile computing have paved the way for new types of distributed applications that can be executed solely by mobile devices on Device-to-Device (D2D) ecosystems (e.g., crowdsensing). Sophisticated applications, like cryptocurrencies, need distr ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2022

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