Sparse Matrix Ordering Algorithms

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 ...

Hypergraph-Partitioning-Based Sparse Matrix Ordering

Introduction In this work we propose novel sparse matrix ordering approaches based on hypergraph partitioning. The significance of hypergraph-partitioning-based (HP-based) ordering is three-fold. First, almost all of the successful nested dissection [6] tools [7, 9, 10] are based on multilevel graph partitioning tools [7, 8, 10] with some extra initial partitioning and refinement strategies spe...

Sparse Matrix Ordering Methods for Interior Point

The main cost of solving a linear programming problem using an interior point method is usually the cost of solving a series of sparse, symmetric linear systems of equations, AA T x = b. These systems are typically solved using a sparse direct method. The rst step in such a method is a reordering of the rows and columns of the matrix to reduce ll in the factor and/or reduce the required work. T...

Parallel Graph Partitioning and Sparse Matrix Ordering Library

Unstructured Graph Partitioning and Sparse Matrix Ordering System

Graph partitioning has extensive applications in many areas, including scientific computing, VLSI design, and task scheduling. The problem is to partition the vertices of a graph in p roughly equal parts, such that the number of edges connecting vertices in different parts is minimized. For example, the solution of a sparse system of linear equations Ax = b via iterative methods on a parallel c...