Isoperimetric Partitioning: A New Algorithm for Graph Partitioning

We present a new algorithm for graph partitioning based on optimization of the combinatorial isoperimetric constant. It is shown empirically that this algorithm is competitive with other global partitioning algorithms in terms of partition quality. The isoperimetric algorithm is easy to parallelize,...

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Bibliographic Details
Published in:SIAM journal on scientific computing Vol. 27; no. 6; pp. 1844 - 1866
Main Authors: Grady, Leo, Schwartz, Eric L.
Format: Journal Article
Language:English
Published: Philadelphia, PA Society for Industrial and Applied Mathematics 01.01.2006
Subjects:
Algorithms
Applied sciences
Exact sciences and technology
Functions of a complex variable
Graphs
Lagrange multiplier
Markov processes
Mathematical analysis
Mathematics
Operational research and scientific management
Operational research. Management science
Portfolio theory
Probability and statistics
Probability theory and stochastic processes
Risk theory. Actuarial science
Sciences and techniques of general use
60J75
30A36
Random walk
Optimization method
Graph theory
91B28
Combinatorial optimization
Competitive algorithms
Graph partitioning
Numerical analysis
Linear equation
Spectral partitioning
isoperimetric problem
91B30
Mathematical programming
linear equations
ISSN:1064-8275, 1095-7197
Online Access:Get full text
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Summary:We present a new algorithm for graph partitioning based on optimization of the combinatorial isoperimetric constant. It is shown empirically that this algorithm is competitive with other global partitioning algorithms in terms of partition quality. The isoperimetric algorithm is easy to parallelize, does not require coordinate information, and handles nonplanar graphs, weighted graphs, and families of graphs which are known to cause problems for other methods. Compared to spectral partitioning, the isoperimetric algorithm is faster and more stable. An exact circuit analogy to the algorithm is also developed with a natural random walks interpretation. The isoperimetric algorithm for graph partitioning is implemented in our publicly available Graph Analysis Toolbox [L. Grady, Ph.D. thesis, Boston University, Boston, MA, 2004], [L. Grady and E. L. Schwartz, Technical report TR-03-021, Boston University, Boston, MA, 2003] for MATLAB obtainable at http://eslab.bu.edu/software/graphanalysis/. This toolbox was used to generate all of the results compiled in the tables of this paper.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1064-8275
1095-7197
DOI:10.1137/040609008