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1990•SIAM Journal on Matrix Analysis and ApplicationsRequires access

A New Algorithm for Finding a Pseudoperipheral Node in a Graph

Roger G. Grimes, Daniel J. Pierce, Horst D. Simon

Open publisher page 34 citations

Abstract

A new algorithm for the computation of a pseudoperipheral node of a graph is presented, and the application of this algorithm to reordering algorithms for the solution of sparse linear systems is discussed. Numerical tests on large sparse matrix problems show the efficiency of the new algorithm. When used for some of the reordering algorithms for reducing the profile and bandwidth of a sparse matrix, the results obtained with the pseudoperipheral nodes of the new algorithm are comparable to the results obtained with the pseudoperipheral nodes produced by the SPARSPAK version of the Gibbs—Poole—Stockmeyer algorithm. The advantage of the new algorithm is that it accesses the adjacency structure of the sparse matrix in a regular pattern. Thus this algorithm is much more suitable both for a parallel and for an out-of-core implementation of the ordering phase for sparse matrix problems.

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What this paper is about

A new algorithm for the computation of a pseudoperipheral node of a graph is presented, and the application of this algorithm to reordering algorithms for the solution of sparse linear systems is discussed. Numerical tests on large sparse matrix problems show the efficiency of the new algorithm. When used for some of the reordering algorithms for reducing the profile and bandwidth of a sparse matrix, the results obtained with the pseudoperipheral nodes of the new algorithm are comparable to the results obtained with the pseudoperipheral nodes produced by the SPARSPAK version of the Gibbs—Poole—Stockmeyer algorithm. The advantage of the new algorithm is that it accesses the adjacency structure of the sparse matrix in a regular pattern. Thus this algorithm is much more suitable both for a parallel and for an out-of-core implementation of the ordering phase for sparse matrix problems.

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OpenAlex reports 34 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

A new algorithm for the computation of a pseudoperipheral node of a graph is presented, and the application of this algorithm to reordering algorithms for the solution of sparse linear systems is discussed. Numerical tests on large sparse matrix problems show the efficiency of the new algorithm. When used for some of the reordering algorithms for reducing the profile and bandwidth of a sparse matrix, the results obtained with the pseudoperipheral nodes of the new algorithm are comparable to the results obtained with the pseudoperipheral nodes produced by the SPARSPAK version of the Gibbs—Poole—Stockmeyer algorithm. The advantage of the new algorithm is that it accesses the adjacency structure of the sparse matrix in a regular pattern. Thus this algorithm is much more suitable both for a parallel and for an out-of-core implementation of the ordering phase for sparse matrix problems.

Key concepts: Adjacency matrix, Algorithm, Cuthill–McKee algorithm, Sparse matrix, Computation, Adjacency list, Matrix (chemical analysis), Computer science

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