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74
A fast and high quality multilevel scheme for partitioning irregular graphs
 SIAM JOURNAL ON SCIENTIFIC COMPUTING
, 1998
"... Recently, a number of researchers have investigated a class of graph partitioning algorithms that reduce the size of the graph by collapsing vertices and edges, partition the smaller graph, and then uncoarsen it to construct a partition for the original graph [Bui and Jones, Proc. ..."
Abstract

Cited by 803 (12 self)
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Recently, a number of researchers have investigated a class of graph partitioning algorithms that reduce the size of the graph by collapsing vertices and edges, partition the smaller graph, and then uncoarsen it to construct a partition for the original graph [Bui and Jones, Proc.
Multilevel hypergraph partitioning: Application in VLSI domain
 IEEE TRANS. VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS
, 1999
"... In this paper, we present a new hypergraphpartitioning algorithm that is based on the multilevel paradigm. In the multilevel paradigm, a sequence of successively coarser hypergraphs is constructed. A bisection of the smallest hypergraph is computed and it is used to obtain a bisection of the origina ..."
Abstract

Cited by 244 (21 self)
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In this paper, we present a new hypergraphpartitioning algorithm that is based on the multilevel paradigm. In the multilevel paradigm, a sequence of successively coarser hypergraphs is constructed. A bisection of the smallest hypergraph is computed and it is used to obtain a bisection of the original hypergraph by successively projecting and refining the bisection to the next level finer hypergraph. We have developed new hypergraph coarsening strategies within the multilevel framework. We evaluate their performance both in terms of the size of the hyperedge cut on the bisection, as well as on the run time for a number of very large scale integration circuits. Our experiments show that our multilevel hypergraphpartitioning algorithm produces highquality partitioning in a relatively small amount of time. The quality of the partitionings produced by our scheme are on the average 6%–23 % better than those produced by other stateoftheart schemes. Furthermore, our partitioning algorithm is significantly faster, often requiring 4–10 times less time than that required by the other schemes. Our multilevel hypergraphpartitioning algorithm scales very well for large hypergraphs. Hypergraphs with over 100 000 vertices can be bisected in a few minutes on today’s workstations. Also, on the large hypergraphs, our scheme outperforms other schemes (in hyperedge cut) quite consistently with larger margins (9%–30%).
Multilevel algorithms for multiconstraint graph partitioning
 In Proceedings of Supercomputing
, 1998
"... ( kirk, karypis, kumar) @ cs.umn.edu ..."
METIS  Unstructured Graph Partitioning and Sparse Matrix Ordering System, Version 2.0
, 1995
"... ..."
Analysis of multilevel graph partitioning
, 1995
"... 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 multileve ..."
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Cited by 91 (13 self)
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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 vertexseparator 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.
Multilevel Circuit Partitioning
 IN PROC. OF THE 34TH ACM/IEEE DESIGN AUTOMATION CONFERENCE
, 1998
"... Many previous works in partitioning have used some underlying clustering algorithm to improve performance. As problem sizes reach new levels of complexity, a single application of a clustering algorithm is insufficient to produce excellent solutions. Recent work has illustrated the promise of multi ..."
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Cited by 82 (8 self)
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Many previous works in partitioning have used some underlying clustering algorithm to improve performance. As problem sizes reach new levels of complexity, a single application of a clustering algorithm is insufficient to produce excellent solutions. Recent work has illustrated the promise of multilevel approaches. A multilevel partitioning algorithm recursively clusters the instance until its size is smaller than a given threshold, then unclusters the instance while applying a partitioning refinement algorithm. In this paper, we propose a new multilevel partitioning algorithm that exploits some of the latest innovations of classical iterative partitioning approaches. Our method also uses a new technique to control the number of levels in our matchingbased clustering algorithm. Experimental results show that our heuristic outperforms numerous existing bipartitioning heuristics with improvements ranging from 6.9 to 27.9 % for 100 runs and 3.0 to 20.6 % for just ten runs (while also using less CPU time). Further, our algorithm generates solutions better than the best known mincut bipartitionings for seven of the ACM/SIGDA benchmark circuits, including golem3 (which has over 100 000 cells). We also present quadrisection results which compare favorably to the partitionings obtained by the GORDIAN cell placement tool. Our work in multilevel quadrisection has been used as the basis for an effective cell placement package.
A TwoDimensional Data Distribution Method For Parallel Sparse MatrixVector Multiplication
 SIAM REVIEW
"... A new method is presented for distributing data in sparse matrixvector multiplication. The method is twodimensional, tries to minimise the true communication volume, and also tries to spread the computation and communication work evenly over the processors. The method starts with a recursive bipar ..."
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Cited by 67 (8 self)
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A new method is presented for distributing data in sparse matrixvector multiplication. The method is twodimensional, tries to minimise the true communication volume, and also tries to spread the computation and communication work evenly over the processors. The method starts with a recursive bipartitioning of the sparse matrix, each time splitting a rectangular matrix into two parts with a nearly equal number of nonzeros. The communication volume caused by the split is minimised. After the matrix partitioning, the input and output vectors are partitioned with the objective of minimising the maximum communication volume per processor. Experimental results of our implementation, Mondriaan, for a set of sparse test matrices show a reduction in communication compared to onedimensional methods, and in general a good balance in the communication work.