NDLI: Interactively Exploring the Connection between Nested Dissection Orderings for Parallel Cholesky Factorization and Vertex Separators

Content Provider	IEEE Xplore Digital Library
Author	Bucker, H.M. Rostami, M.A.
Copyright Year	2014
Description	Author affiliation: Inst. for Comput. Sci., Friedrich Schiller Univ., Jena, Germany (Bucker, H.M.; Rostami, M.A.)
Abstract	Parallel computing is increasingly becoming a core component of undergraduate computing curricula. It is not only part of degree programs in computer science or computer engineering but also in other computational disciplines like computational science and engineering. The underlying concepts of parallel computing affect and interact with many areas of computer science including hardware, software, algorithms, and networking, to name a few. Parallel algorithms for problems arising from scientific computing often involve some combinatorial aspects too. In particular, there is an intimate connection between graph theory and sparse linear algebra. A seemingly serial formulation of a sparse Cholesky factorization can be transformed into a block matrix formulation exhibiting parallelism. This transformation is known as nested dissection ordering and can be expressed in terms of a vertex separator in a suitably defined graph. This paper presents the design and implementation of a novel interactive educational model illustrating this connection for classroom use. The educational module also includes some characteristics of serial games offering a different type of interactive learning in parallel computing education.
Starting Page	1122
Ending Page	1129
File Size	520714
Page Count	8
File Format	PDF
e-ISBN	9781479941162
DOI	10.1109/IPDPSW.2014.125
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2014-05-19
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Symmetric matrices Particle separators EXPLAIN Nested Dissection Ordering Layout Games Parallel processing Interactive Educational Module Software Graph Visualization Parallel Block Cholesky Factorization Sparse matrices
Content Type	Text
Resource Type	Article

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Parallel sparse Cholesky factorization with spectral nested dissection ordering (1994)

Spectral nested dissection (1992).

Comparing Nested Dissection Orderings for Parallel Sparse Matrix Factorization (1995)

Nested-Dissection Orderings for Sparse LU with Partial Pivoting

Parallel Sparse Cholesky Factorization with Spectral Nested Dissection Ordering. Chapter 1

A Cartesian Parallel Nested Dissection Algorithm

On optimal fill-preserving orderings of sparse matrices for parallel cholesky factorizations.

A Fast Algorithm for Reordering Sparse Matrices for Parallel Factorization

Nested dissection orderings for LU factorization with static pivoting

Interactively Exploring the Connection between Nested Dissection Orderings for Parallel Cholesky Factorization and Vertex Separators

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