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- W506101 abstract "Algorithms that find a good partition of highly unstructured graphs are critical in developing efficient algorithms for a wide range of problems in many application areas.In this dissertation we study a class of graph partitioning algorithms that reduce the size of the graph by collapsing vertices and edges, bisect the smaller graph, and then uncoarsen it to construct a bisection for the original graph. We investigate the effectiveness of many different choices for all the three phases of these multilevel recursive bisection graph partitioning algorithms. We also present a new class of multilevel k-way graph partitioning algorithms that directly compute a k-way partition of the coarsest graph. A key innovative feature of our multilevel k-way graph partitioning algorithm is an inexpensive refinement algorithm that can substantially improve upon an initial k-way partition without requiring too much time. We also present the first theoretical analysis that successfully explains certain aspects of the multilevel graph partitioning algorithms, and provides insights as to why these schemes are able to produce very high quality partitions.In this thesis we present parallel formulations both for the multilevel recursive bisection and the multilevel k-way partitioning algorithm. A key feature of our parallel formulation of the multilevel recursive bisection algorithm, is that it uses a two-dimensional distribution of the graph to the processors in order to minimize communication. The key innovative feature of our parallel formulation of the multilevel k-way partitioning algorithm is that it utilizes graph coloring to effectively parallelize both the coarsening phase and the refinement during the uncoarsening phase. Our parallel k-way algorithm, can partition graphs with a million vertices in 128 parts, on a 129-processor Cray T3D in little over two seconds.Factorization algorithms based on threshold incomplete LU factorization have been found to be quite effective in preconditioning iterative system solvers. In this thesis we present a highly parallel formulation of such factorization algorithms. Our algorithm utilizes our parallel multilevel k-way partitioning and independent set computation algorithms to effectively parallelize both the factorization as well as the solution of the resulting triangular systems, used in the application of the preconditioner." @default.
- W506101 created "2016-06-24" @default.
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- W506101 date "1996-01-01" @default.
- W506101 modified "2023-09-26" @default.
- W506101 title "Graph partitioning and its applications to scientific computing" @default.
- W506101 hasPublicationYear "1996" @default.
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