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Directed acyclic graphical models, or DAG models, are widely used to represent complex causal systems. Since the basic task of learning such a model from data is NP-hard, a standard approach is greedy search over the space of directed…
The shortest path problem in graphs is fundamental to AI. Nearly all variants of the problem and relevant algorithms that solve them ignore edge-weight computation time and its common relation to weight uncertainty. This implies that taking…
Laplacian matrices of graphs arise in large-scale computational applications such as machine learning; spectral clustering of images, genetic data and web pages; transportation network flows; electrical resistor circuits; and elliptic…
Subgraph isomorphism counting is an important problem on graphs, as many graph-based tasks exploit recurring subgraph patterns. Classical methods usually boil down to a backtracking framework that needs to navigate a huge search space with…
Synthesis of distributed protocols is a hard, often undecidable, problem. Completion techniques provide partial remedy by turning the problem into a search problem. However, the space of candidate completions is still massive. In this…
Graph analytics elicits insights from large graphs to inform critical decisions for business, safety and security. Several large-scale graph processing frameworks feature efficient runtime systems; however, they often provide programming…
In the recent years, several polynomial algorithms of a dynamical nature have been proposed to address the graph isomorphism problem. In this paper we propose a generalization of an approach exposed in cond-mat/0209112 and find that this…
Directed acyclic graphs (DAGs) constitute a central modeling tool to enable principled reasoning about cause-effect interactions in complex systems. However, since the causal structure underlying a group of variables is often unknown and…
Modern equality saturation systems excel at expression-level rewrites by exploring large spaces of equivalent programs without suffering from the phase-ordering problem. How- ever, these systems struggle to represent equivalence directly…
The paper formalizes a version of parallel online directed acyclic graph (DAG) exploration, general enough to be readily mapped to many computational scenarios. In both the offline and online versions, vertices are weighted with the work…
The graph is one of the most widely used mathematical structures in engineering and science because of its representational power and inherent ability to demonstrate the relationship between objects. The objective of this work is to…
Graph isomorphism problem is a known hard problem. In this paper, a novel randomized algorithm is proposed for this problem which is very simple and fast. It solves the graph isomorphism problem with running time O(n^2.373) for any pair of…
We develop a novel parallel decomposition strategy for unweighted, undirected graphs, based on growing disjoint connected clusters from batches of centers progressively selected from yet uncovered nodes. With respect to similar previous…
We show that every directed graph $G$ with $n$ vertices and $m$ edges admits a directed acyclic graph (DAG) with $m^{1+o(1)}$ edges, called a DAG projection, that can either $(1+1/\text{polylog} (n))$-approximate distances between all pairs…
The growing popularity of dynamic applications such as social networks provides a promising way to detect valuable information in real time. Efficient analysis over high-speed data from dynamic applications is of great significance. Data…
Data augmentations are effective in improving the invariance of learning machines. We argue that the core challenge of data augmentations lies in designing data transformations that preserve labels. This is relatively straightforward for…
The problem of finding an ancestral acyclic directed mixed graph (ADMG) that represents the causal relationships between a set of variables is an important area of research on causal inference. Most existing score-based structure learning…
Graph condensation aims to reduce the size of a large-scale graph dataset by synthesizing a compact counterpart without sacrificing the performance of Graph Neural Networks (GNNs) trained on it, which has shed light on reducing the…
In general, to draw robust conclusions from a dataset, all the analyzed population must be represented on said dataset. Having a dataset that does not fulfill this condition normally leads to selection bias. Additionally, graphs have been…
Large language models (LLMs) have demonstrated remarkable capabilities in a wide range of tasks, yet their application to specialized domains remains challenging due to the need for deep expertise. Retrieval-Augmented generation (RAG) has…