Related papers: Distributed Path Compression for Piecewise Linear …
Lossy compression, widely used by scientists to reduce data from simulations, experiments, and observations, can distort features of interest even under bounded error. Such distortions may compromise downstream analyses and lead to…
This paper presents a well-scaling parallel algorithm for the computation of Morse-Smale (MS) segmentations, including the region separators and region boundaries. The segmentation of the domain into ascending and descending manifolds,…
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 research explores a novel paradigm for preserving topological segmentations in existing error-bounded lossy compressors. Today's lossy compressors rarely consider preserving topologies such as Morse-Smale complexes, and the…
The persistence diagram, which describes the topological features of a dataset, is a key descriptor in Topological Data Analysis. The "Discrete Morse Sandwich" (DMS) method has been reported to be the most efficient algorithm for computing…
We present a distributed-memory library for computations with dense structured matrices. A matrix is considered structured if its off-diagonal blocks can be approximated by a rank-deficient matrix with low numerical rank. Here, we use…
This article describes a geometric partitioning software that can be used for quick computation of data partitions on many-core HPC machines. It is most suited for dynamic applications with load distributions that vary with time.…
We consider the problem of efficiently computing a discrete Morse complex on simplicial complexes of arbitrary dimension and very large size. Based on a common graph-based formalism, we analyze existing data structures for simplicial…
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…
In the segmentation of fine-scale structures from natural and biomedical images, per-pixel accuracy is not the only metric of concern. Topological correctness, such as vessel connectivity and membrane closure, is crucial for downstream…
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 extension of persistent homology to multi-parameter setups is an algorithmic challenge. Since most computation tasks scale badly with the size of the input complex, an important pre-processing step consists of simplifying the input…
We present an efficient distributed memory parallel algorithm for computing connected components in undirected graphs based on Shiloach-Vishkin's PRAM approach. We discuss multiple optimization techniques that reduce communication volume as…
The tensor-train (TT) format is a data-sparse tensor representation commonly used in high dimensional function approximations arising from computational and data sciences. Various sequential and parallel TT decomposition algorithms have…
We present PKT, a new shared-memory parallel algorithm and OpenMP implementation for the truss decomposition of large sparse graphs. A k-truss is a dense subgraph definition that can be considered a relaxation of a clique. Truss…
This paper presents a novel meta algorithm, Partition-Merge (PM), which takes existing centralized algorithms for graph computation and makes them distributed and faster. In a nutshell, PM divides the graph into small subgraphs using our…
We devise achievable encoding schemes for distributed source compression for computing inner products, symmetric matrix products, and more generally, square matrix products, which are a class of nonlinear transformations. To that end, our…
The Massive Parallel Computation (MPC) model is a theoretical framework for popular parallel and distributed platforms such as MapReduce, Hadoop, or Spark. We consider the task of computing a large matching or small vertex cover in this…
Among the novel metrics used to study the relative importance of nodes in complex networks, k-core decomposition has found a number of applications in areas as diverse as sociology, proteinomics, graph visualization, and distributed system…
If learning methods are to scale to the massive sizes of modern datasets, it is essential for the field of machine learning to embrace parallel and distributed computing. Inspired by the recent development of matrix factorization methods…