Related papers: A Parallel Solver for Graph Laplacians

All-pairs similarity problem asks to find all vector pairs in a set of vectors the similarities of which surpass a given similarity threshold, and it is a computational kernel in data mining and information retrieval for several tasks. We…

Discrete variational methods show excellent performance in numerical simulations of different mechanical systems. In this paper, we introduce an iterative procedure for the solution of discrete variational equations for boundary value…

We present a simple spectral approach to the well-studied constrained clustering problem. It captures constrained clustering as a generalized eigenvalue problem with graph Laplacians. The algorithm works in nearly-linear time and provides…

Correlation clustering is a central topic in unsupervised learning, with many applications in ML and data mining. In correlation clustering, one receives as input a signed graph and the goal is to partition it to minimize the number of…

Current algorithms for large-scale industrial optimization problems typically face a trade-off: they either require exponential time to reach optimal solutions, or employ problem-specific heuristics. To overcome these limitations, we…

We consider the minimum-cut partitioning of a graph into more than two parts using spectral methods. While there exist well-established spectral algorithms for this problem that give good results, they have traditionally not been well…

Modeling data sharing in GPU programs is a challenging task because of the massive parallelism and complex data sharing patterns provided by GPU architectures. Better GPU caching efficiency can be achieved through careful task scheduling…

Distributed computing excels at processing large scale data, but the communication cost for synchronizing the shared parameters may slow down the overall performance. Fortunately, the interactions between parameter and data in many problems…

A* is a best-first search algorithm for finding optimal-cost paths in graphs. A* benefits significantly from parallelism because in many applications, A* is limited by memory usage, so distributed memory implementations of A* that use all…

A scalable algorithm for solving compact banded linear systems on distributed memory architectures is presented. The proposed method factorizes the original system into two levels of memory hierarchies, and solves it using parallel cyclic…

This paper proposes a scalable algorithmic framework for spectral reduction of large undirected graphs. The proposed method allows computing much smaller graphs while preserving the key spectral (structural) properties of the original…

In geometry processing, numerical optimization methods often involve solving sparse linear systems of equations. These linear systems have a structure that strongly resembles to adjacency graphs of the underlying mesh. We observe how…

Spectral clustering (SC) is a popular clustering technique to find strongly connected communities on a graph. SC can be used in Graph Neural Networks (GNNs) to implement pooling operations that aggregate nodes belonging to the same cluster.…

This article presents new algorithms for massively parallel granular dynamics simulations on distributed memory architectures using a domain partitioning approach. Collisions are modelled with hard contacts in order to hide their…

The vast amounts of data used in social, business or traffic networks, biology and other natural sciences are often managed in graph-based data sets, consisting of a few thousand up to billions and trillions of vertices and edges,…

Balanced partitioning is often a crucial first step in solving large-scale graph optimization problems, e.g., in some cases, a big graph can be chopped into pieces that fit on one machine to be processed independently before stitching the…

This paper presents a framework that supports the implementation of parallel solutions for the widespread parametric maximum flow computational routines used in image segmentation algorithms. The framework is based on supergraphs, a special…

Recent spectral graph sparsification techniques have shown promising performance in accelerating many numerical and graph algorithms, such as iterative methods for solving large sparse matrices, spectral partitioning of undirected graphs,…

Many graph problems can be solved using ordered parallel graph algorithms that achieve significant speedup over their unordered counterparts by reducing redundant work. This paper introduces a new priority-based extension to GraphIt, a…

Algorithms for finding minimum or bounded vertex covers in graphs use a branch-and-reduce strategy, which involves exploring a highly imbalanced search tree. Prior GPU solutions assign different thread blocks to different sub-trees, while…