Related papers: Rule-based Graph Repair using Minimally Restricted…
Correlation Clustering is an elegant model that captures fundamental graph cut problems such as Min $s-t$ Cut, Multiway Cut, and Multicut, extensively studied in combinatorial optimization. Here, we are given a graph with edges labeled $+$…
A connected undirected graph $G = (V,E)$ is lower conformally rigid if uniform edge weights maximize the second smallest Laplacian eigenvalue $\lambda_2(w)$ over all normalized edge weights $w$, and upper conformally rigid if uniform edge…
Graph transformation formalisms have proven to be suitable tools for the modelling of chemical reactions. They are well established in theoretical studies and increasingly also in practical applications in chemistry. The latter is made…
We introduce and study a mathematical framework for a broad class of regularization functionals for ill-posed inverse problems: Regularization Graphs. Regularization graphs allow to construct functionals using as building blocks linear…
Graph transformation systems have the potential to be realistic models of chemistry, provided a comprehensive collection of reaction rules can be extracted from the body of chemical knowledge. A first key step for rule learning is the…
Graph modification problems, which aim to find a small set of modifications to a graph so that it satisfies a desired property, have been studied for several special graph classes. The literature is rather rich in NP-completeness results…
Graph convolutional neural networks (GCNNs) have emerged as powerful tools for analyzing graph-structured data, achieving remarkable success across diverse applications. However, the theoretical understanding of the stability of these…
We consider regenerating codes in distributed storage systems where connections between the nodes are constrained by a graph. In this problem, the failed node downloads the information stored at a subset of vertices of the graph for the…
Given two subsets A and B of nodes in a directed graph, the conduciveness of the graph from A to B is the ratio representing how many of the edges outgoing from nodes in A are incoming to nodes in B. When the graph's nodes stand for the…
The basic (and traditional) crossing number problem is to determine the minimum number of crossings in a topological drawing of an input graph in the plane. We develop a unified framework yielding fixed-parameter tractable (FPT) algorithms…
Graph processes model a number of important problems such as identifying the epicenter of an earthquake or predicting weather. In this paper, we propose a Graph Convolutional Recurrent Neural Network (GCRNN) architecture specifically…
A set $D\subseteq V$ of a graph $G=(V,E)$ is called a restrained dominating set of $G$ if every vertex not in $D$ is adjacent to a vertex in $D$ and to a vertex in $V \setminus D$. The \textsc{Minimum Restrained Domination} problem is to…
Regularization has become a primary tool for developing reliable estimators of the covariance matrix in high-dimensional settings. To curb the curse of dimensionality, numerous methods assume that the population covariance (or inverse…
The objective of graph coarsening is to generate smaller, more manageable graphs while preserving key information of the original graph. Previous work were mainly based on the perspective of spectrum-preserving, using some predefined…
In a data exchange setting with target constraints, it is often the case that a given source instance has no solutions. In such cases, the semantics of target queries trivialize. The aim of this paper is to introduce and explore a new…
Sequential learning with feedback graphs is a natural extension of the multi-armed bandit problem where the problem is equipped with an underlying graph structure that provides additional information - playing an action reveals the losses…
We study here a natural situation when constraint programming can be entirely reduced to rule-based programming. To this end we explain first how one can compute on constraint satisfaction problems using rules represented by simple…
We present a graph neural network model for solving graph-to-graph learning problems. Most deep learning on graphs considers ``simple'' problems such as graph classification or regressing real-valued graph properties. For such tasks, the…
When studying networks using random graph models, one is sometimes faced with situations where the notion of adjacency between nodes reflects multiple constraints. Traditional random graph models are insufficient to handle such situations.…
The Constraint Satisfaction Problem (CSP) is a problem of computing a homomorphism $\mathbf{R}\to \mathbf{\Gamma}$ between two relational structures, where $\mathbf{R}$ is defined over a domain $V$ and $\mathbf{\Gamma}$ is defined over a…