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Analysis of multilevel graph partitioning (1995)

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by George Karypis , Vipin Kumar
Citations:78 - 13 self
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@TECHREPORT{Karypis95analysisof,
    author = {George Karypis and Vipin Kumar},
    title = {Analysis of multilevel graph partitioning},
    institution = {},
    year = {1995}
}

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Abstract

Recently, a number of researchers have investigated a class of algorithms that are based on multilevel graph partitioning that have moderate computational complexity, and provide excellent graph partitions. However, there exists little theoretical analysis that could explain the ability of multilevel algorithms to produce good partitions. In this paper we present such an analysis. We show under certain reasonable assumptions that even if no refinement is used in the uncoarsening phase, a good bisection of the coarser graph is worse than a good bisection of the finer graph by at most a small factor. We also show that the size of a good vertex-separator of the coarse graph projected to the finer graph (without performing refinement in the uncoarsening phase) is higher than the size of a good vertexseparator of the finer graph by at most a small factor.

Citations

864 An Efficient Heuristic Procedure for Partitioning Graphs - Kernighan, Lin - 1970
616 A fast and high quality multilevel scheme for partitioning irregular graphs - Karypis, Kumar - 1999
445 Introduction to Parallel Computing: Design and Analysis of Algorithms - Grama, Karypis, et al. - 2003
437 Partitioning sparse matrices with eigenvectors of graphs - Pothen, Simon, et al. - 1990
428 Computer Solution of Large Sparse Positive Definite Systems - George, Liu - 1981
376 Multilevel k-way partitioning scheme for irregular graphs - Karypis, Kumar - 1998
367 A multi-level algorithm for partitioning graphs - Hendrickson, Leland - 1995
338 A separator theorem for planar graphs - Lipton, Tarjan - 1979
254 A fast multilevel implementation of recursive spectral bisection for partitioning unstructured problems.In - Barnard, Simon - 1993
118 Modification of the minimum degree algorithm by multiple elimination - Liu - 1985
102 Parallel algorithms for sparse linear systems - Heath, Ng, et al. - 1991
100 Highly scalable parallel algorithms for sparse matrix factorization - Gupta, Karypis, et al. - 1993
99 MeTiS unstructured graph partitioning and sparse matrix ordering system version 2.0 - Karypis, Kumar - 1995
83 A unified geometric approach to graph separators - Miller, Teng, et al. - 1991
73 Finding small simple cycle separators for 2-connected planar graphs - Miller - 1986
69 Automatic mesh partitioning - Miller, Teng, et al. - 1993
66 The Chaco user’s guide version 1.0 - Hendrickson, Leland - 1993
60 A heuristic for reducing fill in sparse matrix factorization - Bui, Jones - 1993
51 Solving finite element equations on concurrent computers - Nour-Omid, Raefsky, et al. - 1986
50 Aspects of unstructured grids and finite-volume solvers for the euler and navier-strokes equations. In AGARD Report 787on Unstructured Grid Methods for Advection Dominated Flows - Barth - 1992
41 Parallel algorithms for dynamically partitioning unstructured grids - Diniz, Plimpton, et al. - 1995
33 Towards a fast implementation of spectral nested dissection - Pothen, Simon, et al. - 1992
30 PMRSB: Parallel Multilevel Recursive Specral Bisection - Barnard - 1995
30 A parallel graph partitioning algorithm for a message-passing multiprocessor - Gilbert, Zmijewski - 1987
23 A Cartesian parallel nested dissection algorithm - Heath, Raghavan - 1992
20 A parallel implementation of multilevel recursive spectral bisection for application to adaptive unstructured meshes - Barnard, Simon - 1995
12 Parallel ordering using edge contraction - Raghavan - 1995
11 A Cartesian nested dissection algorithm - MT, Raghavan - 1995
9 and Padma Raghavan. A Cartesian parallel nested dissection algorithm - Heath - 1995
4 Finite element methods on the connection machine cm-5 system - Johan, Mathur, et al. - 1993
2 A parallel implementtaion of the multiple minimum degree ordering heuristic - Ghose, Rothberg - 1994
1 A fast multilevel implementationof recursive spectral bisection for partitioningunstructuredproblems - Barnard, Simon - 1993
1 Computer Solutionof LargeSparsePositive Definite Systems - Liu - 1981
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