Related papers: Aggregative Coarsening for Multilevel Hypergraph P…
The new class of alternating-conjugate splitting methods is presented and analyzed. They are obtained by concatenating a given composition involving complex coefficients with the same composition but with the complex conjugate coefficients.…
Two fundamental algorithm-design paradigms are Tree Search and Dynamic Programming. The techniques used therein have been shown to complement one another when solving the complete set partitioning problem, also known as the coalition…
The balanced hypergraph partitioning problem (HGP) is to partition the vertex set of a hypergraph into k disjoint blocks of bounded weight, while minimizing an objective function defined on the hyperedges. Whereas real-world applications…
Multi-constraint hypergraph partitioning is a generalization of balanced partitioning, where the vertex set of a hypergraph is partitioned such that the inter-block connectivity of hyperedges is minimized while balancing the vertices with…
Hypergraph partitioning lies at the heart of a number of problems in machine learning and network sciences. Many algorithms for hypergraph partitioning have been proposed that extend standard approaches for graph partitioning to the case of…
Coded matrix multiplication is a technique to enable straggler-resistant multiplication of large matrices in distributed computing systems. In this paper, we first present a conceptual framework to represent the division of work amongst…
Large-scale graphs are widely used to represent object relationships in many real world applications. The occurrence of large-scale graphs presents significant computational challenges to process, analyze, and extract information. Graph…
This study addresses the challenge of simulating realistic particle systems by proposing a novel particle decomposition scheme that improves the parallel performance of surface resolved particle simulations. Realistic particle systems often…
The efficient solution of sparse, linear systems resulting from the discretization of partial differential equations is crucial to the performance of many physics-based simulations. The algorithmic optimality of multilevel approaches for…
We introduce a finite element method for numerical upscaling of second order elliptic equations with highly heterogeneous coefficients. The method is based on a mixed formulation of the problem and the concepts of the domain decomposition…
Processing large complex networks like social networks or web graphs has recently attracted considerable interest. In order to do this in parallel, we need to partition them into pieces of about equal size. Unfortunately, previous parallel…
Segmentation of ultra-high resolution images is increasingly demanded, yet poses significant challenges for algorithm efficiency, in particular considering the (GPU) memory limits. Current approaches either downsample an ultra-high…
In this paper, we discuss the convergence of an Algebraic MultiGrid (AMG) method for general symmetric positive-definite matrices. The method relies on an aggregation algorithm, named \emph{coarsening based on compatible weighted matching},…
This paper introduces a novel approach to algebraic multigrid methods for large systems of linear equations coming from finite element discretizations of certain elliptic second order partial differential equations. Based on a discrete…
A nonlinear multigrid solver for two-phase flow and transport in a mixed fractional-flow velocity-pressure-saturation formulation is proposed. The solver, which is under the framework of the full approximation scheme (FAS), extends our…
Integrating data from heterogeneous sources is often modeled as merging graphs. Given two or more 'compatible', but not-isomorphic graphs, the first step is to identify a graph alignment, where a potentially partial mapping of vertices…
Hypergraph matching has recently become a popular approach for solving correspondence problems in computer vision as it allows to integrate higher-order geometric information. Hypergraph matching can be formulated as a third-order…
Partitioning is a known problem in computer science and is critical in chip design workflows, as advancements in this area can significantly influence design quality and efficiency. Deep Learning (DL) techniques, particularly those…
Multigrid methods have proven to be an invaluable tool to efficiently solve large sparse linear systems arising in the discretization of partial differential equations (PDEs). Algebraic multigrid methods and in particular adaptive algebraic…
Streamline-based quad meshing algorithms use smooth cross fields to partition surfaces into quadrilateral regions by tracing cross field separatrices. In practice, re-entrant corners and misalignment of singularities lead to small regions…