Matrix decomposition on the star graph

A.-E. Al-Ayyoub, K. Day
1997 IEEE Transactions on Parallel and Distributed Systems  
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(N 3 /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 n ( ) ! , each with approximately n! nodes. The proposed
more » ... l 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.
doi:10.1109/71.605767 fatcat:poyomvnha5dt3kz4tatolf7qm4