Vertex Separators for Partitioning a Graph

Permuting Sparse Square Matrices into Block Diagonal Form with Overlap

In this whitepaper, we describe the problem of permuting sparse square matrices into block diagonal form with overlap (BDO) and propose a graph partitioning algorithm for solving this problem. A block diagonal matrix with overlap is a block diagonal matrix whose consecutive diagonal blocks may overlap. The objective in this permutation problem is to minimize the total overlap size, whereas the ...

oGPVS/BDO: A Software Package for Ordered Graph Partitioning by Vertex Separators and Permuting Matrices into Block Diagonal Form with Overlap

Graph Partitioning Algorithms with Applications to Scientific Computing Graph Partitioning Algorithms

Identifying the parallelism in a problem by partitioning its data and tasks among the processors of a parallel computer is a fundamental issue in parallel computing. This problem can be modeled as a graph partitioning problem in which the vertices of a graph are divided into a speciied number of subsets such that few edges join two vertices in diierent subsets. Several new graph partitioning al...

Partitioning Hypergraphs in Scientific Computing Applications through Vertex Separators on Graphs

The modeling flexibility provided by hypergraphs has drawn a lot of interest from the combinatorial scientific community, leading to novel models and algorithms, their applications, and development of associated tools. Hypergraphs are now a standard tool in combinatorial scientific computing. The modeling flexibility of hypergraphs however, comes at a cost: algorithms on hypergraphs are inheren...

Partitioning Multivariate Polynomial Equations via Vertex Separators for Algebraic Cryptanalysis and Mathematical Applications

We present a novel approach for solving systems of polynomialequations via graph partitioning. The concept of a variable-sharing graph of asystem of polynomial equations is defined. If such graph is disconnected, thenthe system of equations is actually two separate systems that can be solvedindividually. This can provide a significant speed-up in computing the solutionto the...