Related papers: Load Balancing using Hilbert Space-filling Curves …
Partitioning graphs into blocks of roughly equal size such that few edges run between blocks is a frequently needed operation in processing graphs. Recently, size, variety, and structural complexity of these networks has grown dramatically.…
Space-filling curves (SFCs) are used in high performance computing to distribute a computational domain or its mesh, respectively, amongst different compute units, i.e.~cores or nodes or accelerators. The part of the domain allocated to…
Furthering our understanding of many of today's interesting problems in plasma physics---including plasma based acceleration and magnetic reconnection with pair production due to quantum electrodynamic effects---requires large-scale kinetic…
Hilbert's two-dimensional space-filling curve is appreciated for its good locality properties for many applications. However, it is not clear what is the best way to generalize this curve to filling higher-dimensional spaces. We argue that…
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…
General Matrix Multiplication (GEMM) is the cornerstone of HPC workloads and Deep Learning. State-of-the-art vendor libraries tune tensor layouts, parallelization schemes, and cache blocking to minimize data movement across the memory…
Hilbert-space fragmentation provides a mechanism for ergodicity breaking in quantum many-body systems even in the absence of disorder, leading to dynamically disconnected sectors and strong memory of initial conditions. However, identifying…
Scheduling query execution plans is a particularly complex problem in shared-nothing parallel systems, where each site consists of a collection of local time-shared (e.g., CPU(s) or disk(s)) and space-shared (e.g., memory) resources and…
A space-filling function is a bijection from the unit line segment to the unit square, cube, or hypercube. The function from the unit line segment is continuous. The inverse function, while well-defined, is not continuous. Space-filling…
Distribution comparison plays a central role in many machine learning tasks like data classification and generative modeling. In this study, we propose a novel metric, called Hilbert curve projection (HCP) distance, to measure the distance…
Partitioning graphs into blocks of roughly equal size such that few edges run between blocks is a frequently needed operation when processing graphs on a parallel computer. When a topology of a distributed system is known an important task…
This work is related to PHG (Parallel Hierarchical Grid). PHG is a toolbox for developing parallel adaptive finite element programs, which is under active development at the State Key Laboratory of Scientific and Engineering Computing. The…
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…
In order to be able to process the increasing amount of spatial data, efficient methods for their handling need to be developed. One major challenge for big spatial data is access. This can be achieved through space-filling curves, as they…
Accurate molecular sequence analysis is a key task in the field of bioinformatics. To apply molecular sequence classification algorithms, we first need to generate the appropriate representations of the sequences. Traditional numeric…
We propose an algorithm based on Hilbert space-filling curves to reorder mesh elements in memory for use with the Spectral Element Method, aiming to attain fewer cache misses, better locality of data reference and faster execution. We…
A parallel computer system is a collection of processing elements that communicate and cooperate to solve large computational problems efficiently. To achieve this, at first the large computational problem is partitioned into several tasks…
We describe Hilbert's spacefilling curve in several different ways: as an automatic sequence of directions,as a regular and synchronized sequence of coordinates of lattice points encountered, and as an automatic bitmap image.
Starting with a similarity function between objects, it is possible to define a distance metric on pairs of objects, and more generally on probability distributions over them. These distance metrics have a deep basis in functional analysis,…
In this work, we propose an adaptive geometric multigrid method for the solution of large-scale finite cell flow problems. The finite cell method seeks to circumvent the need for a boundary-conforming mesh through the embedding of the…