Issue No. 08 - August (1997 vol. 8)
ISSN: 1045-9219
pp: 803-812
ABSTRACT
<p><b>Abstract</b>—We present and evaluate, for the first time, a parallel algorithm for solving the LU decomposition problem on the star graph. The proposed parallel algorithm is of <it>O</it>(<it>N</it><super>3</super>/<it>n</it>!) computation complexity and uses <it>O</it>(<it>Nn</it>) communication time to decompose a matrix of order <it>N</it> on a star graph of dimension <it>n</it>, where <it>N</it>≥ (<it>n</it>− 1)!. The incurred communication time is better than the best known results for the hypercube, <it>O</it>(<it>N log n</it>!), and the mesh, <tmath>$O(N\sqrt {n!}),$</tmath> each with approximately <it>n</it>! nodes. The proposed parallel algorithm takes advantage of the attractive topological qualities of the star graph in order to reduce the communication time involved in tasks such as pivoting, row/column interchanges, and pivot row and multipliers column broadcasts.</p>
INDEX TERMS
Interconnection networks, matrix decomposition, parallel processing, star graphs.
CITATION
Abdel-Elah Al-Ayyoub, Khaled Day, "Matrix Decomposition on the Star Graph", IEEE Transactions on Parallel & Distributed Systems, vol. 8, no. , pp. 803-812, August 1997, doi:10.1109/71.605767