Concept

Produit tensoriel (graphe)

Publications associées (14)

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

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

Learning anisotropic filters on product graphs

Pascal Frossard, Clément Arthur Yvon Vignac

The extension of convolutional neural networks to irregular domains has pavedthe way to promising graph data analysis methods. It has however come at theexpense of a reduced representation power, as most of these new network archi-tectures can only learn i ...

2019

Stationary time-vertex signal processing

Nathanaël Perraudin, Andreas Loukas

This paper considers regression tasks involving high-dimensional multivariate processes whose structure is dependent on some known graph topology. We put forth a new definition of time-vertex wide-sense stationarity, or joint stationarity for short, that g ...

2019

A time-reversible integrator for the time-dependent Schrödinger equation on an adaptive grid

Jiri Vanicek, Seonghoon Choi

One of the most accurate methods for solving the time-dependent Schrödinger equation uses a combination of the dynamic Fourier method with the split-operator algorithm on a tensor-product grid. To reduce the number of required grid points, we let the grid ...

2019

Graph-based Methods for Visualization and Clustering

Johann Paratte

The amount of data that we produce and consume is larger than it has been at any point in the history of mankind, and it keeps growing exponentially. All this information, gathered in overwhelming volumes, often comes with two problematic characteristics: ...

EPFL2017

Reconstruction using approximate message passing methods

Paul Hurley, Matthieu Martin Jean-André Simeoni, Giovanni Cherubini, Sanaz Kazemi

The present invention is notably directed to a computer-implemented method for image reconstruction. The method comprises: accessing elements that respectively correspond to measurement values, which can be respectively mapped to measurement nodes; and per ...

2017

A Dichotomy for Real Weighted Holant Problems

Sangxia Huang

Holant is a framework of counting characterized by local constraints. It is closely related to other well-studied frameworks such as the counting constraint satisfaction problem (#CSP) and graph homomorphism. An effective dichotomy for such frameworks can ...

Springer Basel Ag2016

Asynchronous Decoding of LDPC Codes over BEC

Amin Karbasi, Amir Hesam Salavati, Saeid Haghighatshoar

LDPC codes are typically decoded by running a synchronous message passing algorithm over the corresponding bipartite factor graph (made of variable and check nodes). More specifically, each synchronous round consists of 1) updating all variable nodes based ...

2015

On some coloring problems in grids

Dominique de Werra

We study complexity issues related to some coloring problems in grids: we examine in particular the case of List coloring, of Precoloring extension and of (p, q)-List coloring, the case of List coloring in bipartite graphs where lists in the first part of ...

2013

Correlation-Aware Reconstruction of Network Coded Sources

Pascal Frossard, Nikolaos Thomos, Eirina Bourtsoulatze

In this paper, we consider the problem of decoding network coded correlated data when the decoder does not receive sufficient information for exact decoding. We propose an iterative decoding algorithm based on belief propagation that efficiently exploits t ...

2012

Product Multicommodity Flow in Wireless Networks

Olivier Lévêque

We provide a tight approximate characterization of the n-dimensional product multicommodity flow (PMF) region for a wireless network of n nodes. Separate characterizations in terms of the spectral properties of appropriate network graphs are obtained in bo ...

2008

Codes, graphs and graph based codes

Andrew Brown

This work is concerned with codes, graphs and their links. Graph based codes have recently become very prominent in both information theory literature and practical applications. While most research has centered around their performance under iterative dec ...

EPFL2007

Some graph products and their expansion properties

Mohammad Amin Shokrollahi, Andrew Brown

We introduce "derandomized" versions of the tensor product and the zig-zag product, extending the ideas in the derandomized squaring operation of Rozenman and Vadhan. These enable us to obtain graphs with smaller degrees than those obtained using their non ...

2006