Results 1 
5 of
5
A fast and high quality multilevel scheme for partitioning irregular graphs
 SIAM JOURNAL ON SCIENTIFIC COMPUTING
, 1998
"... Recently, a number of researchers have investigated a class of graph partitioning algorithms that reduce the size of the graph by collapsing vertices and edges, partition the smaller graph, and then uncoarsen it to construct a partition for the original graph [Bui and Jones, Proc. ..."
Abstract

Cited by 797 (12 self)
 Add to MetaCart
Recently, a number of researchers have investigated a class of graph partitioning algorithms that reduce the size of the graph by collapsing vertices and edges, partition the smaller graph, and then uncoarsen it to construct a partition for the original graph [Bui and Jones, Proc.
How Good is Recursive Bisection?
 SIAM J. Sci. Comput
, 1995
"... . The most commonly used pway partitioning method is recursive bisection (RB). It first divides a graph or a mesh into two equal sized pieces, by a "good" bisection algorithm, and then recursively divides the two pieces. Ideally, we would like to use an optimal bisection algorithm. Because the opti ..."
Abstract

Cited by 84 (4 self)
 Add to MetaCart
. The most commonly used pway partitioning method is recursive bisection (RB). It first divides a graph or a mesh into two equal sized pieces, by a "good" bisection algorithm, and then recursively divides the two pieces. Ideally, we would like to use an optimal bisection algorithm. Because the optimal bisection problem, that partitions a graph into two equal sized subgraphs to minimize the number of edges cut, is NPcomplete, practical RB algorithms use more efficient heuristics in place of an optimal bisection algorithm. Most such heuristics are designed to find the best possible bisection within allowed time. We show that the recursive bisection method, even when an optimal bisection algorithm is assumed, may produce a pway partition that is very far way from the optimal one. Our negative result is complemented by two positive ones: First we show that for some important classes of graphs that occur in practical applications, such as wellshaped finite element and finite difference...
Geometric Spectral Partitioning
, 1995
"... We investigate a new method for partitioning a graph into two equalsized pieces with few connecting edges. We combine ideas from two recently suggested partitioning algorithms, spectral bisection (which uses an eigenvector of a matrix associated with the graph) and geometric bisection (which applie ..."
Abstract

Cited by 13 (1 self)
 Add to MetaCart
We investigate a new method for partitioning a graph into two equalsized pieces with few connecting edges. We combine ideas from two recently suggested partitioning algorithms, spectral bisection (which uses an eigenvector of a matrix associated with the graph) and geometric bisection (which applies to graphs that are meshes in Euclidean space). The new method does not require geometric coordinates, and it produces partitions that are often better than either the spectral or geometric ones.
A separatorbased framework for automated partitioning and mapping of parallel algorithms for numerical solution of PDEs
 In Proc.1992 DAGS/PC Symposium
, 1992
"... This paper is a report on ongoing work in developing automated systems for the partitioning, placement, and routing of data that is necessary for the e cient parallel solution of large problems in scienti c computing, speci cally the numerical solution of partial di erential equations. Many of these ..."
Abstract

Cited by 11 (5 self)
 Add to MetaCart
This paper is a report on ongoing work in developing automated systems for the partitioning, placement, and routing of data that is necessary for the e cient parallel solution of large problems in scienti c computing, speci cally the numerical solution of partial di erential equations. Many of these problems have as an iterated inner loop the formation of the product of a large sparse matrix and a vector of variables. This problem of sparse matrixvector multiplication has an underlying combinatorial graph structure that can be exploited. Using geometric information from the original problem, we can partition this combinatorial graph using provably good two or threedimensional graph sep
Large Numerical Linear Algebra in 1994: The Continuing Influence of Parallel Computing
 In Proceedings of the 1994 Scalable High Performance Computing Conference
, 1994
"... This note covers two aspects of the state of the art of large numerical linear algebra problems. Firstly, we look at the current records for sparse and dense linear systems and eigenvalue problems on a variety of machines. Our second subject matter is perhaps more of a question than an answer. Here ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
This note covers two aspects of the state of the art of large numerical linear algebra problems. Firstly, we look at the current records for sparse and dense linear systems and eigenvalue problems on a variety of machines. Our second subject matter is perhaps more of a question than an answer. Here we explore why network topologies of a parallel machine are hardly ever used in ways that perhaps a graph theorist might envision, especially given that linear algebra, particularly dense linear algebra, consists of many very regular predictable operations. 1 Introduction This work represents in part a continuation of previous linear algebra surveys [4, 5]. My hope is to heighten awareness of relevant issues associated with numerical linear algebra that might be lost in the rush to write fast programs. Perhaps like the sports sections of any newspaper, I research the linear algebra records, discuss important issues associated with modern computing, but do not use this space to teach you how ...