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Recent years have witnessed the emerging success of graph neural networks (GNNs) for modeling structured data. However, most GNNs are designed for homogeneous graphs, in which all nodes and edges belong to the same types, making them…
Increasingly modern data science platforms today have non-intrusive and extensible provenance ingestion mechanisms to collect rich provenance and context information, handle modifications to the same file using distinguishable versions, and…
Graph representation learning has achieved a remarkable success in many graph-based applications, such as node classification, link prediction, and community detection. These models are usually designed to preserve the vertex information at…
A directed graph $G=(V,E)$ is {\it strongly pseudo transitive} if there is a partition $\{A,E-A\}$ of $E$ so that graphs $G_1=(V,A)$ and $G_2=(V,E-A)$ are transitive, and additionally, if $ab\in A$ and $bc\in E $ implies that $ac\in E$. A…
Graph-based methods are known to be successful in many machine learning and pattern classification tasks. These methods consider semi-structured data as graphs where nodes correspond to primitives (parts, interest points, segments, etc.)…
Combining ideas from distributed algorithms and alternating automata, we introduce a new class of finite graph automata that recognize precisely the languages of finite graphs definable in monadic second-order logic. By restricting…
Directed acyclic graph (DAG) models are widely used to represent causal relationships among random variables in many application domains. This paper studies a special class of non-Gaussian DAG models, where the conditional variance of each…
Transductions are a general formalism for expressing transformations of graphs (and more generally, of relational structures) in logic. We prove that a graph class $\mathscr{C}$ can be $\mathsf{FO}$-transduced from a class of bounded-height…
Directed acyclic graph (DAG) models, also called Bayesian networks, impose conditional independence constraints on a multivariate probability distribution, and are widely used in probabilistic reasoning, machine learning and causal…
Recent progress in cross-lingual relation and event extraction use graph convolutional networks (GCNs) with universal dependency parses to learn language-agnostic sentence representations such that models trained on one language can be…
We prove a robust contraction decomposition theorem for $H$-minor-free graphs, which states that given an $H$-minor-free graph $G$ and an integer $p$, one can partition in polynomial time the vertices of $G$ into $p$ sets $Z_1,\dots,Z_p$…
Recent years have witnessed the impressive progress in Neural Dependency Parsing. According to the different factorization approaches to the graph joint probabilities, existing parsers can be roughly divided into autoregressive and…
We present a canonical way to decompose finite graphs into highly connected local parts. The decomposition depends only on an integer parameter whose choice sets the intended degree of locality. The global structure of the graph, as…
The problem of learning a directed acyclic graph (DAG) up to Markov equivalence is equivalent to the problem of finding a permutation of the variables that induces the sparsest graph. Without additional assumptions, this task is known to be…
Orienting the edges of an undirected graph such that the resulting digraph satisfies some given constraints is a classical problem in graph theory, with multiple algorithmic applications. In particular, an $st$-orientation orients each edge…
The problem of orienting the edges of an undirected graph such that the resulting digraph is acyclic and has a single source s and a single sink t has a long tradition in graph theory and is central to many graph drawing algorithms. Such an…
Transformer-based models have recently shown success in representation learning on graph-structured data beyond natural language processing and computer vision. However, the success is limited to small-scale graphs due to the drawbacks of…
Let $G$ be a finite group. Denoting by ${\rm{cd}}(G)$ the set of the degrees of the irreducible complex characters of $G$, we consider the {\it character degree graph} of $G$: this is the (simple, undirected) graph whose vertices are the…
Daily internet communication relies heavily on tree-structured graphs, embodied by popular data formats such as XML and JSON. However, many recent generative (probabilistic) models utilize neural networks to learn a probability distribution…
Motivated by the increasing need to understand the algorithmic foundations of distributed large-scale graph computations, we study a number of fundamental graph problems in a message-passing model for distributed computing where $k \geq 2$…