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Matrix Decomposition on the Star Graph
August 1997 (vol. 8 no. 8)
pp. 803-812

Abstract—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 O(N3/n!) computation complexity and uses O(Nn) communication time to decompose a matrix of order N on a star graph of dimension n, where N≥ (n− 1)!. The incurred communication time is better than the best known results for the hypercube, O(N log n!), and the mesh, $O(N\sqrt {n!}),$ each with approximately n! 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.

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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 and Distributed Systems, vol. 8, no. 8, pp. 803-812, Aug. 1997, doi:10.1109/71.605767
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