Journal Article10.1145/355841.355845
An Implementation of a Pseudoperipheral Node Finder
Alan George,Joseph W. H. Liu +1 more
99
TL;DR: The objective in this paper is to provide a well-structured flexible implementat ion of this algori thm which includes some .modifications tha t appear to improve its performance and include some experiments demonstra t ing the effect of various modifications to the original algorithm.
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Abstract: Many algorithms for finding orderings for sparse symmetr ic matrices operate on the corresponding undirected graph. These algorithms often require one or more \"start ing nodes,\" and for some algorithms experience suggests tha t nodes which are at maximum or nearly maximum distance apar t are good candidates [4, 611]. In a recent paper, Gibbs et al. [8] provide a novel heuristic algorithm for finding such nodes. Our objective in this paper is to provide a well-structured flexible implementat ion of this algori thm which includes some .modifications tha t appear to improve its performance. We include some experiments demonstra t ing the effect of various modifications to the original algorithm. We now give some formal definitions and a precise s ta tement of the problem. Let G ffi (X, E) be an undirected graph with the set X of nodes and the set E of undirected edges represented as unordered pairs of nodes. A path of length k is an ordered set of distinct nodes (Xo, x l , . . . , Xk) where {x,-1, x,) E E for 1 _< i _ k. A graph is connected if for each pair of distinct nodes there is a path joining them. Throughou t this paper, graphs are assumed to be connected unless we state otherwise. Consider a connected graph G. The distance d(x, y) between two nodes x and y in G is defined to be the length of a shortest pa th connecting them. Following Berge [2], we define the eccentricity of a node x to be the quant i ty l(x) ffi max{d(x, y) [ y E X}.
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Citations
Direct methods for sparse matrices
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An algorithm for profile and wavefront reduction of sparse matrices
TL;DR: Empirical evidence suggests that the new algorithm is superior to existing methods for profile and wavefront reduction, it is fast, requires only a small amount of memory, and is simple to program.
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Implementation of the Gibbs-Poole-Stockmeyer and Gibbs-King Algorithms
TL;DR: A new FORTRAN implementation of the Gibbs-King method, ACM Algorithm 582, which is portable, faster, more reliable, and which uses less storage, is described.
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Ordering symmetric sparse matrices for small profile and wavefront
John Reid,Jennifer A. Scott +1 more
TL;DR: This paper looks at the computation of pseudoperipheral nodes and compares the effectiveness of using an algorithm based on level-set structures with using the spectral method as the basis of the Reverse Cuthill–McKee algorithm for bandwidth reduction.
References
Reducing the bandwidth of sparse symmetric matrices
E. Cuthill,J. McKee +1 more
- 26 Aug 1969
TL;DR: A direct method of obtaining an automatic nodal numbering scheme to ensure that the corresponding coefficient matrix will have a narrow bandwidth is presented.
1.6K
An algorithm for reducing the bandwidth and profile of a sparse matrix
TL;DR: Extensive testing on finite element matrices indicates that the algorithm typically produces bandwidth and profile which are comparable to those of the commonly-used reverse Cuthill–McKee algorithm, yet requires significantly less computation time.
638
Comparative Analysis of the Cuthill–McKee and the Reverse Cuthill–McKee Ordering Algorithms for Sparse Matrices
Wai-Hung Liu,Andrew H. Sherman +1 more
TL;DR: It is proved that for band elimination methods, the two orderings are equivalent and that, surprisingly, the reverse ordering is always at least as good as the original one when envelope elimination techniques are used.
304
Algorithms for Matrix Partitioning and the Numerical Solution of Finite Element Systems
Alan D. George,Joseph W. H. Liu +1 more
TL;DR: In this paper, a sparse positive definite system of equations arising from the use of the finite element method to solve a two-dimensional boundary value problem is defined, and a common method of solving these equations is to use a finite element approach.
67
Algorithm 508: Matrix Bandwidth and Profile Reduction [F1]
TL;DR: This program was extensively tested and compared with several other programs and was found to be considerably faster than the others, generally superior for bandwidth reduction and as satisfactory as any other for profile reduction.
41