Graph partitioning models for parallel computing
Bruce Hendrickson,Tamara G. Kolda +1 more
- 01 Nov 2000
- Vol. 26, Iss: 12, pp 1519-1534
TL;DR: A survey of recently proposed alternatives for graph partitioning finds that the standard methodology for graph partitions minimizes the wrong metric and lacks expressibility.
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Abstract: Calculations can naturally be described as graphs in which vertices represent computation and edges reflect data dependencies. By partitioning the vertices of a graph, the calculation can be divided among processors of a parallel computer. However, the standard methodology for graph partitioning minimizes the wrong metric and lacks expressibility. We survey several recently proposed alternatives and discuss their relative merits.
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Citations
Direct methods for sparse matrices
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References
A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
George Karypis,Vipin Kumar +1 more
TL;DR: This work presents a new coarsening heuristic (called heavy-edge heuristic) for which the size of the partition of the coarse graph is within a small factor of theSize of the final partition obtained after multilevel refinement, and presents a much faster variation of the Kernighan--Lin (KL) algorithm for refining during uncoarsening.
An efficient heuristic procedure for partitioning graphs
Brian W. Kernighan,Shou-De Lin +1 more
TL;DR: A heuristic method for partitioning arbitrary graphs which is both effective in finding optimal partitions, and fast enough to be practical in solving large problems is presented.
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Some simplified NP-complete graph problems
TL;DR: This paper shows that a number of NP - complete problems remain NP -complete even when their domains are substantially restricted, and determines essentially the lowest possible upper bounds on node degree for which the problems remainNP -complete.
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A Multi-Level Algorithm For Partitioning Graphs
Bruce Hendrickson,Robert W. Leland +1 more
- 08 Dec 1995
TL;DR: A multilevel algorithm for graph partitioning in which the graph is approximated by a sequence of increasingly smaller graphs, and the smallest graph is then partitioned using a spectral method, and this partition is propagated back through the hierarchy of graphs.
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Multilevel hypergraph partitioning: application in VLSI domain
George Karypis,Rajat Aggarwal,Vipin Kumar,Shashi Shekhar +3 more
- 13 Jun 1997
TL;DR: The experiments show that the multilevel hypergraph partitioning algorithm produces high quality partitioning in relatively small amount of time and outperforms other schemes (in hyperedge cut) quite consistently with larger margins.
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