Related papers: Graph Width Measures for CNF-Encodings with Auxili…

We demonstrate a new connection between e-graphs and Boolean circuits. This allows us to adapt existing literature on circuits to easily arrive at an algorithm for optimal e-graph extraction, parameterized by treewidth, which runs in…

An important question in the study of constraint satisfaction problems (CSP) is understanding how the graph or hypergraph describing the incidence structure of the constraints influences the complexity of the problem. For binary CSP…

Graph neural networks (GNNs) have shown great success in learning from graph-based data. The key mechanism of current GNNs is message passing, where a node's feature is updated based on the information passing from its local neighbourhood.…

The enormous amount of data to be represented using large graphs exceeds in some cases the resources of a conventional computer. Edges in particular can take up a considerable amount of memory as compared to the number of nodes. However,…

In this report, we propose a quick survey of the currently known techniques for encoding a Boolean cardinality constraint into a CNF formula, and we discuss about the relevance of these encodings. We also propose models to facilitate…

Graph Neural Networks (GNNs) have shown remarkable performance on graph-structured data. However, recent empirical studies suggest that GNNs are very susceptible to distribution shift. There is still significant ambiguity about why…

Graph neural networks (GNNs) are effective machine learning models for many graph-related applications. Despite their empirical success, many research efforts focus on the theoretical limitations of GNNs, i.e., the GNNs expressive power.…

Partitioning a graph using graph separators, and particularly clique separators, are well-known techniques to decompose a graph into smaller units which can be treated independently. It was previously known that the treewidth was bounded…

We consider the problem of learning the structure of undirected graphical models with bounded treewidth, within the maximum likelihood framework. This is an NP-hard problem and most approaches consider local search techniques. In this…

Mim-width and sim-width are among the most powerful graph width parameters, with sim-width more powerful than mim-width, which is in turn more powerful than clique-width. While several $\mathsf{NP}$-hard graph problems become tractable for…

Current graph representation learning techniques use Graph Neural Networks (GNNs) to extract features from dataset embeddings. In this work, we examine the quality of these embeddings and assess how changing them can affect the accuracy of…

The constraint complexity of a graphical realization of a linear code is the maximum dimension of the local constraint codes in the realization. The treewidth of a linear code is the least constraint complexity of any of its cycle-free…

Twin-width is a recently formulated graph and matrix invariant that intuitively quantifies how far a graph is from having the structural simplicity of a co-graph. Since its introduction in 2020, twin-width has received increasing attention…

Fixed parameter tractable (FPT) algorithms run in time f(p(x)) poly(|x|), where f is an arbitrary function of some parameter p of the input x and poly is some polynomial function. Treewidth, branchwidth, cliquewidth, NLC-width, rankwidth,…

We present a class of linear programming approximations for constrained optimization problems. In the case of mixed-integer polynomial optimization problems, if the intersection graph of the constraints has bounded tree-width our…

We present new results on the size of OBDD representations of structurally characterized classes of CNF formulas. First, we identify a natural sufficient condition, which we call the few subterms property, for a class of CNFs to have…

Many recent works address the question of characterizing induced obstructions to bounded treewidth. In 2022, Lozin and Razgon completely answered this question for graph classes defined by finitely many forbidden induced subgraphs. Their…

Many hard graph problems can be solved efficiently when restricted to graphs of bounded treewidth, and more generally to graphs of bounded clique-width. But there is a price to be paid for this generality, exemplified by the four problems…

The capacity of unifilar finite-state channels in the presence of feedback is investigated. We derive a new evaluation method to extract graph-based encoders with their achievable rates, and to compute upper bounds to examine their…

Despite the recent advances of graph neural networks (GNNs) in modeling graph data, the training of GNNs on large datasets is notoriously hard due to the overfitting. Adversarial training, which augments data with the worst-case adversarial…