Related papers: Aggregative Coarsening for Multilevel Hypergraph P…

We study the approximability of an existing framework for clustering edge-colored hypergraphs, which is closely related to chromatic correlation clustering and is motivated by machine learning and data mining applications where the goal is…

Solving Algebra Problems with Geometry Diagrams (APGDs) is still a challenging problem because diagram processing is not studied as intensively as language processing. To work against this challenge, this paper proposes a hologram reasoning…

We present a shared-memory algorithm to compute high-quality solutions to the balanced $k$-way hypergraph partitioning problem. This problem asks for a partition of the vertex set into $k$ disjoint blocks of bounded size that minimizes the…

Problems from graph drawing, spectral clustering, network flow and graph partitioning can all be expressed in terms of graph Laplacian matrices. There are a variety of practical approaches to solving these problems in serial. However, as…

Graph Transformers (GTs) have made remarkable achievements in graph-level tasks. However, most existing works regard graph structures as a form of guidance or bias for enhancing node representations, which focuses on node-central…

Graph-based clustering methods have demonstrated the effectiveness in various applications. Generally, existing graph-based clustering methods first construct a graph to represent the input data and then partition it to generate the…

Hypergraph partitioning is a recurring NP-hard problem in engineering; its efficient solution at scale hinges on parallelism. This work proposes a GPU-centric algorithm for multi-level hypergraph partitioning aimed at a specific set of…

Scalability of graph neural networks remains one of the major challenges in graph machine learning. Since the representation of a node is computed by recursively aggregating and transforming representation vectors of its neighboring nodes…

This paper considers the balanced hypergraph partitioning problem, which asks for partitioning the vertices into $k$ disjoint blocks of bounded size while minimizing an objective function over the hyperedges. Here, we consider the most…

Large-scale parallel numerical simulations are essential for a wide range of engineering problems that involve complex, coupled physical processes interacting across a broad range of spatial and temporal scales. The data structures involved…

Hardware accelerators, such as those based on GPUs and FPGAs, offer an excellent opportunity to efficiently parallelize functionalities. Recently, modern embedded platforms started being equipped with such accelerators, resulting in a…

Modern graph or network datasets often contain rich structure that goes beyond simple pairwise connections between nodes. This calls for complex representations that can capture, for instance, edges of different types as well as so-called…

We propose a multilevel approach for trace systems resulting from hybridized discontinuous Galerkin (HDG) methods. The key is to blend ideas from nested dissection, domain decomposition, and high-order characteristic of HDG discretizations.…

Graph mining analyzes real-world graphs to find core substructures (connected subgraphs) in applications modeled as graphs. Substructure discovery is a process that involves identifying meaningful patterns, structures, or components within…

Attributed graphs model real networks by enriching their nodes with attributes accounting for properties. Several techniques have been proposed for partitioning these graphs into clusters that are homogeneous with respect to both semantic…

Modern supercomputers are increasingly requiring the presence of accelerators and co-processors. However, it has not been easy to achieve good performance on such heterogeneous clusters. The key challenge has been to ensure good load…

Partitioning a graph into blocks of roughly equal weight while cutting only few edges is a fundamental problem in computer science with numerous practical applications. While shared-memory parallel partitioners have recently matured to…

The ability to differentiate through optimization problems has unlocked numerous applications, from optimization-based layers in machine learning models to complex design problems formulated as bilevel programs. It has been shown that…

Multi-view clustering is an important approach to analyze multi-view data in an unsupervised way. Among various methods, the multi-view subspace clustering approach has gained increasing attention due to its encouraging performance.…

We present an algebraic method for constructing a highly effective coarse grid correction to accelerate domain decomposition. The coarse problem is constructed from the original matrix and a small set of input vectors that span a low-degree…