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We study the scalability of consensus-based distributed optimization algorithms by considering two questions: How many processors should we use for a given problem, and how often should they communicate when communication is not free?…

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…

Graph Neural Networks (GNNs) have achieved state-of-the-art (SOTA) performance in diverse domains. However, training GNNs on large-scale graphs poses significant challenges due to high memory demands and significant communication overhead…

The last decade has witnessed an explosion in the development of models, theory and computational algorithms for "big data" analysis. In particular, distributed computing has served as a natural and dominating paradigm for statistical…

Graph neural networks (GNNs) are widely used for learning node embeddings in graphs, typically adopting a message-passing scheme. This approach, however, leads to the neighbor explosion problem, with exponentially growing computational and…

We propose a novel approach to iterated sparse matrix dense matrix multiplication, a fundamental computational kernel in scientific computing and graph neural network training. In cases where matrix sizes exceed the memory of a single…

We consider the PC-algorithm Spirtes et. al. (2000) for estimating the skeleton of a very high-dimensional acyclic directed graph (DAG) with corresponding Gaussian distribution. The PC-algorithm is computationally feasible for sparse…

Graph neural networks are often used to model interacting dynamical systems since they gracefully scale to systems with a varying and high number of agents. While there has been much progress made for deterministic interacting systems,…

Graph Retrieval Augmented Generation (GRAG) is a novel paradigm that takes the naive RAG system a step further by integrating graph information, such as knowledge graph (KGs), into large-scale language models (LLMs) to mitigate…

Motivated by the increasing need to understand the distributed algorithmic foundations of large-scale graph computations, we study some fundamental graph problems in a message-passing model for distributed computing where $k \geq 2$…

Massive Multiple-Input Multiple-Out (MIMO) detection is an important problem in modern wireless communication systems. While traditional Belief Propagation (BP) detectors perform poorly on loopy graphs, the recent Graph Neural Networks…

Distributed signal processing has attracted widespread attention in the scientific community due to its several advantages over centralized approaches. Recently, graph signal processing has risen to prominence, and adaptive distributed…

Graph Neural Network (GNNs) based methods have recently become a popular tool to deal with graph data because of their ability to incorporate structural information. The only hurdle in the performance of GNNs is the lack of labeled data.…

Recently continuous relaxations have been proposed in order to learn Directed Acyclic Graphs (DAGs) from data by backpropagation, instead of using combinatorial optimization. However, a number of techniques for fully discrete…

We introduce an effective algorithmic method for the computation of a lower bound for uniform expansion in one-dimensional dynamics. The approach employs interval arithmetic and thus provides a rigorous numerical result (computer-assisted…

Retrieval-Augmented Generation (RAG) is a powerful technique for enhancing Large Language Models (LLMs) with external, up-to-date knowledge. Graph RAG has emerged as an advanced paradigm that leverages graph-based knowledge structures to…

Motivated by the increasing need for fast processing of large-scale graphs, we study a number of fundamental graph problems in a message-passing model for distributed computing, called $k$-machine model, where we have $k$ machines that…

Approximate nearest neighbor search (ANNS) is a fundamental problem in databases and data mining. A scalable ANNS algorithm should be both memory-efficient and fast. Some early graph-based approaches have shown attractive theoretical…

DAG (directed acyclic graph) tasks are widely used to model parallel real-time workload. The real-time performance of a DAG task not only depends on its total workload, but also its graph structure. Intuitively, with the same total…

Efficient layout of large-scale graphs remains a challenging problem: the force-directed and dimensionality reduction-based methods suffer from high overhead for graph distance and gradient computation. In this paper, we present a new graph…