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

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.