scholarly journals A Distributed-Memory Package for Dense Hierarchically Semi-Separable Matrix Computations Using Randomization

2016 ◽  
Vol 42 (4) ◽  
pp. 1-35 ◽  
Author(s):  
François-Henry Rouet ◽  
Xiaoye S. Li ◽  
Pieter Ghysels ◽  
Artem Napov
Keyword(s):  
Distributed Memory ◽  
Matrix Computations ◽  
Separable Matrix

Parallel Matrix Computations.

1986 ◽  
Author(s):  
G. W. Stewart ◽  
Dianne P. O'Leary
Keyword(s):  
Matrix Computations

Large Sparse Stable Matrix Computations

1990 ◽  
Author(s):  
Alex Pothen ◽  
Jesse L. Barlow
Keyword(s):  
Matrix Computations ◽  
Stable Matrix

Implementing actor-based primitives on distributed-memory architectures

1991 ◽  
Vol 2 (2) ◽  
pp. 45-49 ◽  
Author(s):  
Michele Di Santo ◽  
Giulio Iannello
Keyword(s):  
Distributed Memory ◽  
Memory Architectures

scholarly journals Practical Wavelet Tree Construction

2021 ◽  
Vol 26 ◽  
pp. 1-67
Author(s):  
Patrick Dinklage ◽  
Jonas Ellert ◽  
Johannes Fischer ◽  
Florian Kurpicz ◽  
Marvin Löbel
Keyword(s):  
Parallel Algorithms ◽  
Shared Memory ◽  
Distributed Memory ◽  
Auxiliary Information ◽  
Parallel Computers ◽  
External Memory ◽  
Sequential Algorithms ◽  
Bottom Up ◽  
Memory Efficiency ◽  
Tree Construction

We present new sequential and parallel algorithms for wavelet tree construction based on a new bottom-up technique. This technique makes use of the structure of the wavelet trees—refining the characters represented in a node of the tree with increasing depth—in an opposite way, by first computing the leaves (most refined), and then propagating this information upwards to the root of the tree. We first describe new sequential algorithms, both in RAM and external memory. Based on these results, we adapt these algorithms to parallel computers, where we address both shared memory and distributed memory settings. In practice, all our algorithms outperform previous ones in both time and memory efficiency, because we can compute all auxiliary information solely based on the information we obtained from computing the leaves. Most of our algorithms are also adapted to the wavelet matrix , a variant that is particularly suited for large alphabets.

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