K. Eswar, P. Sadayappan, and V. Visvanathan, "Multifrontal Factorization of Sparse Matrices on Shared Memory Multiprocessors", pp. 159-166, in Proc. 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of the input matrix. An early processor mapping algorithm which attempts to reduce inter process communication is subtree to subcube [34, 36] which works well for balanced tree topologies. Later research efforts have improved upon the load balancing aspects for more general elimination trees [29, 32, 50, 55, 75, 76, 81]. Our static partitioning heuristic shares similarities with several of these methods. In less predictable environments than a dedicated homogeneous system, or even in less efficient communication architectures where contention induces large communication imbalances (e.g. software shared memory ....

K. Eswar, P. Sadayappan, and V. Visvanathan, "Multifrontal Factorization of Sparse Matrices on Shared Memory Multiprocessors", pp. 159-166, in Proc. 1991.

....values, with care being taken to ensure postive definiteness. The next step in the sequential part is to be determine the mapping of the columns of the matrix to processors. This is done by constructing a tree called the elimination tree [84] and using a heuristic called recursive partitioning [35, 36]. The mapping algorithm maps supernodes to groups of processors. The nodes in each supernode are distributed among the processors in its assigned group in a block fashion, causing the creation of minisupernodes on each processor. Nodes in a minisupernode will also have the property of sharing a ....

K. Eswar, P. Sadayappan, and V. Visvanathan. Multifrontal factorization of sparse matrices on shared-memory multiprocessors. In Proceedings of the Twentieth International Conference on Parallel Processing, volume III, pages 159--166, St. Charles, IL, 1991.

....The mapping of data and computation along with local scheduling of computation within each processor has to be performed. In this paper, we focus on ordering strategies for sparse factorization. In actual experiments, the mapping of data has been performed using a recursive partitioning algorithm [3] that generates a good mapping for recursively partitionable processor networks such as the hypercube. Scheduling of computation is constrained by the data dependences among the columns of the Cholesky factor. Structural information about the reordered matrix can be represented in a compact form ....

K. Eswar, P. Sadayappan, and V. Visvanathan. Multifrontal Factorization of Sparse Matrices on SharedMemory Multiprocessors. In International Conference on Parallel Processing, pages 159--166, 1991.

....algorithm [8] is used to generate a low fill ordering. An equivalent ordering is then produced that preserves the fill structure, but is more suitable for parallel factorization [12, 14, 17, 18] Mapping algorithms attempt to map the nodes in an elimination tree to a finite number of processors [2, 4, 9, 20]. Independent subtrees of the elimination tree correspond to independent subproblems that can be solved in parallel without incurring any communication between them. The objective of the mapping algorithms is to attempt to achieve load balance and minimize communication costs. Previous approaches ....

....bin packing algorithm for mapping arbitrary trees [4] Pothen et al. 20] introduced the proportional mapping algorithm that maps independent subtrees of the elimination tree to sets of processors such that the number of processors assigned to a subtree is proportional to its weight. Eswar et al. [2] proposed a recursive partitioning algorithm that maps nodes in unstructured elimination trees to a recursively partitionable network with a finite number of processors. 3 Heuristic clustering algorithm We present a heuristic ordering and mapping algorithm that performs a perfect elimination ....

K. Eswar, P. Sadayappan, and V. Visvanathan. Multifrontal Factorization of Sparse Matrices on SharedMemory Multiprocessors. In International Conference on Parallel Processing, volume 3, pages 159--166, 1991.

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K. Eswar, P. Sadayappan, and V. Visvanathan. Multifrontal factorization of sparse matrices on shared-memory multiprocessors. In International Conference on Parallel Processing, pages 159--166, 1991.

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K. Eswar, P. Sadayappan, and V. Visvanathan. Multifrontal factorization of sparse matrices on shared-memory multiprocessors. In International Conference on Parallel Processing, volume 3, pages 159--166, 1991. 10

....that are approximately in the same proportion as the sizes of the t daughter composite processors. When this occurs, the algorithm is recursively applied to each of the t sets of subtrees using the corresponding subtree in the composite processor tree. The recursive partitioning mapping algorithm [7] is a special case of the above nested mapping algorithm in which the composite processor tree is a complete binary tree, and the the group of processors associated with each node is equally split between its two daughters. This section is concluded with some more comments on the appropriateness ....

....Local aggr. 146 9158 Global aggr. 3083 77815 Total 5840 265241 7 Related work Various previous works have addressed the use of index based mapping strategies for dense matrix factorization [14, 9, 1] Several researchers have also proposed nested mapping strategies for sparse matrix factorization [12, 10, 16, 7]. The combination of index based mapping and nested mapping strategies has been studied in34 dependently by other researchers in specific contexts. In [13] a mapping strategy for a multifrontal algorithm [5, 15] is presented that combines a two dimensional partitioning of the matrix with a ....

K. Eswar, P. Sadayappan, and V. Visvanathan, "Multifrontal factorization of sparse matrices on shared-memory multiprocessors," Proceedings of the Twentieth International Conference on Parallel Processing, St. Charles, IL, Vol. III, pp. 159-166, 1991.

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