%0 Journal Article %1 808.65148 %A Hendrickson, Bruce A. %A Womble, David E. %D 1994 %J SIAM J. Sci. Comput. %K algorithms algorithms; assignment block-torus-wrap; dense mapping; matrix parallel scalable scheme; torus-wrap %N 5 %P 1201-1226 %T The torus-wrap mapping for dense matrix calculations on massively parallel computers. %V 15 %X Scalable parallel algorithms are considered for linear algebra applications. A bottleneck in these algorithms is the mapping of matrix elements to processors. Wrapping a block mapping in both rows and columns of the matrix is called the torus-wrap mapping. Its generalization is the block-torus-wrap, which assigns each block to a single processor in such a way that the distribution of block mirrors is the distribution of elements in a torus-wrap mapping. It is proved that this assignment scheme leads to dense matrix algorithms that achieve the lower bound on interprocessor communication under reasonable conditions. Theoretical and experimental results are compared with those obtained from more traditional mapping.

@article{808.65148, abstract = {Scalable parallel algorithms are considered for linear algebra applications. A bottleneck in these algorithms is the mapping of matrix elements to processors. Wrapping a block mapping in both rows and columns of the matrix is called the torus-wrap mapping. Its generalization is the block-torus-wrap, which assigns each block to a single processor in such a way that the distribution of block mirrors is the distribution of elements in a torus-wrap mapping. It is proved that this assignment scheme leads to dense matrix algorithms that achieve the lower bound on interprocessor communication under reasonable conditions. Theoretical and experimental results are compared with those obtained from more traditional mapping. }, added-at = {2008-03-02T02:12:02.000+0100}, author = {Hendrickson, Bruce A. and Womble, David E.}, biburl = {https://www.bibsonomy.org/bibtex/245fe424a4fa14b962814eecb5ebb12a9/dmartins}, classmath = {*65Y05 Parallel computation (numerical methods) 65F05 Direct methods for linear systems 68P10 Searching and sorting}, description = {robotica-bib}, interhash = {e5598de1d4d895756c82d1a3a759adaf}, intrahash = {45fe424a4fa14b962814eecb5ebb12a9}, journal = {SIAM J. Sci. Comput.}, keywords = {algorithms algorithms; assignment block-torus-wrap; dense mapping; matrix parallel scalable scheme; torus-wrap}, language = {English}, number = 5, pages = {1201-1226}, reviewer = {L.S.Ioffe (Haifa)}, timestamp = {2008-03-02T02:13:05.000+0100}, title = {The torus-wrap mapping for dense matrix calculations on massively parallel computers. }, volume = 15, year = 1994 }