Multilevel Algorithm for Graph Partitioning

A class of multilevel algorithms for partitioning of a sparse matrix prior to parallel solution of a system of linear equations is described. This matrix partitioning problem can be described in terms of a graph partitioning problem which is known to be NP-hard, so several heuristics for its solutio...

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Bibliographic Details
Published inMatrix Methods: Theory, Algorithms And Applications pp. 433 - 448
Main Authors Bochkarev, N. S., Diyankov, O. V., Pravilnikov, V. Y.
Format Book Chapter
LanguageEnglish
Published WORLD SCIENTIFIC 01.04.2010
Subjects
Matrices and Applications
graph partitioning
load balancing
parallel computations
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ISBN9812836020
9789812836014
9812836012
9814469556
9789812836021
9789814469555
DOI10.1142/9789812836021_0028

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Summary:A class of multilevel algorithms for partitioning of a sparse matrix prior to parallel solution of a system of linear equations is described. This matrix partitioning problem can be described in terms of a graph partitioning problem which is known to be NP-hard, so several heuristics for its solution have been proposed in the past decades. For this purpose we use the multilevel algorithm proposed by B. Hendrickson and R. Leland [2] and further developed by G. Karypis and V. Kumar [3]. This algorithm is very efficient and tends to produce high quality partitioning for a wide range of matrices arising in many practical applications.
ISBN:9812836020
9789812836014
9812836012
9814469556
9789812836021
9789814469555
DOI:10.1142/9789812836021_0028