Algorithms 62-64. Graph-theoretic algorithms for sparse matrix transformations

Generic Graph Algorithms for Sparse Matrix Ordering

Fill-reducing sparse matrix orderings have been a topic of active research for many years. Although most such algorithms are developed and analyzed within a graph-theoretical framework, for reasons of performance the corresponding implementations are typically realized with programming languages devoid of language features necessary to explicitly represent graph abstractions. Recently, generic ...

13. Implementing Sparse Matrices for Graph Algorithms

Sparse matrices are a key data structure for implementing graph algorithms using linear algebra. This chapter reviews and evaluates storage formats for sparse matrices and their impact on primitive operations. We present complexity results of these operations on different sparse storage formats both in the random access memory (RAM) model and in the input/output (I/O) model. RAM complexity resu...

GDAGsim: Sparse matrix algorithms for Bayesian computation

GDAGsim is a software library which can be used to carry out conditional sampling of linear Gaussian directed acyclic graph models, and hence can be used for the implementation of efficient block MCMC samplers for such models. This paper examines the software library and its design, and how it can be applied to problems in Bayesian inference.

Sparse Matrix Reordering Algorithms for Cluster Identification

Combinatorial Algorithms for Parallel Sparse Matrix Distributions

Combinatorial algorithms have long played a crucial enabling role in parallel computing. An important problem in sparse matrix computations is how to distribute the sparse matrix and vectors among processors. We review graph, bipartite graph, and hypergraph models for both 1d (row or column) distributions and 2d distributions. A valuable tool is hypergraph partitioning. We present results using...