Related papers: Simple parallel and distributed algorithms for spe…

We present an amelioration of current known algorithms for optimal spectral partitioning problems. The idea is to use the advantage of a representation using density functions while decreasing the computational time. This is done by…

We give a parallel $O(\log(n))$-time algorithm on a CRCW PRAM to assign vertical and horizontal segments to the vertices of any planar bipartite graph $G$ in the following manner: i) Two segments cannot share an interior point ii) Two…

Stochastic optimization algorithms update models with cheap per-iteration costs sequentially, which makes them amenable for large-scale data analysis. Such algorithms have been widely studied for structured sparse models where the sparsity…

Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…

Because of the significant increase in size and complexity of the networks, the distributed computation of eigenvalues and eigenvectors of graph matrices has become very challenging and yet it remains as important as before. In this paper…

In this note, we test the performance of six algorithms from the family of graph-based splitting methods [SIAM J. Optim., 34 (2024), pp. 1569-1594] specialized to normal cones of linear subspaces. To do this, we first implement some…

The state-of-the-art deep neural networks (DNNs) have significant computational and data management requirements. The size of both training data and models continue to increase. Sparsification and pruning methods are shown to be effective…

A $t$-spanner of a graph is a subgraph that $t$-approximates pairwise distances. The greedy algorithm is one of the simplest and most well-studied algorithms for constructing a sparse spanner: it computes a $t$-spanner with $n^{1+O(1/t)}$…

Graph coloring has been broadly used to discover concurrency in parallel computing. To speedup graph coloring for large-scale datasets, parallel algorithms have been proposed to leverage modern GPUs. Existing GPU implementations either have…

In this paper, we consider the problem of counting and sampling structures in graphs. We define a class of "edge universal labeling problems"---which include proper $k$-colorings, independent sets, and downsets---and describe simple…

This paper presents a simple and efficient approach for finding the bridges and failure points in a densely connected network mapped as a graph. The algorithm presented here is a parallel algorithm which works in a distributed environment.…

Graph learning from data represents a canonical problem that has received substantial attention in the literature. However, insufficient work has been done in incorporating prior structural knowledge onto the learning of underlying…

The notion of vertex sparsification is introduced in \cite{M}, where it was shown that for any graph $G = (V, E)$ and a subset of $k$ terminals $K \subset V$, there is a polynomial time algorithm to construct a graph $H = (K, E_H)$ on just…

Motivated by performance optimization of large-scale graph processing systems that distribute the graph across multiple machines, we consider the balanced graph partitioning problem. Compared to the previous work, we study the…

Distributed algorithms are often beset by the straggler effect, where the slowest compute nodes in the system dictate the overall running time. Coding-theoretic techniques have been recently proposed to mitigate stragglers via algorithmic…

Graphs naturally appear in several real-world contexts including social networks, the web network, and telecommunication networks. While the analysis and the understanding of graph structures have been a central area of study in algorithm…

Cut and spectral sparsification of graphs have numerous applications, including e.g. speeding up algorithms for cuts and Laplacian solvers. These powerful notions have recently been extended to hypergraphs, which are much richer and may…

We propose an approach to graph sparsification based on the idea of preserving the smallest $k$ eigenvalues and eigenvectors of the Graph Laplacian. This is motivated by the fact that small eigenvalues and their associated eigenvectors tend…

We prove that every graph has a spectral sparsifier with a number of edges linear in its number of vertices. As linear-sized spectral sparsifiers of complete graphs are expanders, our sparsifiers of arbitrary graphs can be viewed as…

In this work we propose a simple and easily parallelizable algorithm for multiway graph partitioning. The algorithm alternates between three basic components: diffusing seed vertices over the graph, thresholding the diffused seeds, and then…