Related papers: Engineering Data Reduction for Nested Dissection

Recently, graph neural networks (GNNs) have gained much attention as a growing area of deep learning capable of learning on graph-structured data. However, the computational and memory requirements for training GNNs on large-scale graphs…

In this work, we develop a new fast algorithm, spaQR -- sparsified QR, for solving large, sparse linear systems. The key to our approach is using low-rank approximations to sparsify the separators in a Nested Dissection based Householder QR…

Matrix factorization is an inference problem that has acquired importance due to its vast range of applications that go from dictionary learning to recommendation systems and machine learning with deep networks. The study of its fundamental…

We present a matrix-factorization algorithm that scales to input matrices with both huge number of rows and columns. Learned factors may be sparse or dense and/or non-negative, which makes our algorithm suitable for dictionary learning,…

This paper considers the network slicing (NS) problem which attempts to map multiple customized virtual network requests to a common shared network infrastructure and allocate network resources to meet diverse service requirements. This…

The minimum cut problem for an undirected edge-weighted graph asks us to divide its set of nodes into two blocks while minimizing the weight sum of the cut edges. Here, we introduce a linear-time algorithm to compute near-minimum cuts. Our…

The parallel ordering of large graphs is a difficult problem, because on the one hand minimum degree algorithms do not parallelize well, and on the other hand the obtainment of high quality orderings with the nested dissection algorithm…

We describe algorithms to efficiently compute minimum $(s,t)$-cuts and global minimum cuts of undirected surface-embedded graphs. Given an edge-weighted undirected graph $G$ with $n$ vertices embedded on an orientable surface of genus $g$,…

Ordering vertices of a graph is key to minimize fill-in and data structure size in sparse direct solvers, maximize locality in iterative solvers, and improve performance in graph algorithms. Except for naturally parallelizable ordering…

The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…

Computations, where the number of results is much smaller than the input data and are produced through some sort of accumulation, are called Reductions. Reductions appear in many scientific applications. Usually, reductions admit an…

The shortest paths problem is a fundamental challenge in graph theory, with a broad range of potential applications. The algorithms based on matrix multiplication exhibits excellent parallelism and scalability, but is constrained by high…

The procedure of Least Square-Errors curve fitting is extensively used in many computer applications for fitting a polynomial curve of a given degree to approximate a set of data. Although various methodologies exist to carry out curve…

Distributed systems can be found in various applications, e.g., in robotics or autonomous driving, to achieve higher flexibility and robustness. Thereby, data flow centric applications such as Deep Neural Network (DNN) inference benefit…

In this paper we show how graph structure can be used to drastically reduce the computational bottleneck of the Breadth First Search algorithm (the foundation of many graph traversal techniques). In particular, we address parallel…

Large models and enormous data are essential driving forces of the unprecedented successes achieved by modern algorithms, especially in scientific computing and machine learning. Nevertheless, the growing dimensionality and model…

In numerical linear algebra, considerable effort has been devoted to obtaining faster algorithms for linear systems whose underlying matrices exhibit structural properties. A prominent success story is the method of generalized nested…

We consider the fundamental problem of decomposing a large-scale approximate nearest neighbor search (ANNS) problem into smaller sub-problems. The goal is to partition the input points into neighborhood-preserving shards, so that the…

This paper studies reduced-order modeling of dynamic networks with strongly connected topology. Given a graph clustering of an original complex network, we construct a quotient graph with less number of vertices, where the edge weights are…

Efficient retrieval of information is of key importance when using Big Data systems. In large scale-out data architectures, data are distributed and replicated across several machines. Queries/tasks to such data architectures, are sent to a…