An Improved Spectral Graph Partitioning Algorithm for Mapping Parallel Computations

Efficient use of a distributed memory parallel computer requires that the computational load be balanced across processors in a way that minimizes interprocessor communication. A new domain mapping algorithm is presented that extends recent work in which ideas from spectral graph theory have been ap...

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Bibliographic Details
Published in:SIAM journal on scientific computing Vol. 16; no. 2; pp. 452 - 469
Main Authors: Hendrickson, Bruce, Leland, Robert
Format: Journal Article
Language:English
Published: Philadelphia, PA Society for Industrial and Applied Mathematics 01.03.1995
Subjects:
Algorithms
Applied sciences
Assignment problem
Combinatorics
Combinatorics. Ordered structures
Communication
Computer science; control theory; systems
Cost control
Decomposition
Eigenvectors
Exact sciences and technology
Graph theory
Information retrieval. Graph
Laboratories
Mathematics
Methods
Methods of scientific computing (including symbolic computation, algebraic computation)
Numerical analysis. Scientific computation
Optimization
Sciences and techniques of general use
Theoretical computing
Finite element method
Parallel algorithm
Spectral method
Grid pattern
Eigenvector
Hypercube
Decomposition method
Graph theory
Finite difference method
ISSN:1064-8275, 1095-7197
Online Access:Get full text
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Summary:Efficient use of a distributed memory parallel computer requires that the computational load be balanced across processors in a way that minimizes interprocessor communication. A new domain mapping algorithm is presented that extends recent work in which ideas from spectral graph theory have been applied to this problem. The generalization of spectral graph bisection involves a novel use of multiple eigenvectors to allow for division of a computation into four or eight parts at each stage of a recursive decomposition. The resulting method is suitable for scientific computations like irregular finite elements or differences performed on hypercube or mesh architecture machines. Experimental results confirm that the new method provides better decompositions arrived at more economically and robustly than with previous spectral methods. This algorithm allows for arbitrary nonnegative weights on both vertices and edges to model inhomogeneous computation and communication. A new spectral lower bound for graph bisection is also presented.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1064-8275
1095-7197
DOI:10.1137/0916028