Asymptotically Tight Bounds for Performing BMMC Permutations on Parallel Disk Systems

d Abstract) Thomas H. Cormen Leonard F. Wisniewski Department of Mathematics and Computer Science Dartmouth College We give asymptotically equal lower and upper bounds for the number of parallel I/O operations required to perform BMMC permutations (de ned by a characteristic matrix that is nonsingular over GF(2)) on parallel disk systems. Underthe Vitter-Shriver parallel-disk model with N records, D disks, block size B, and M records of RAM, we show a universal lower bound of ; N BD ; 1 + rank( ) lg(M=B) parallel I/Os for performing a BMMC permutation, where is the lower left lg(N=B) lgB submatrix of the characteristic matrix. We adapt this lower bound to show that the algorithm for BPC permutations in Cor93] is asymptotically optimal. We also present an algorithm that uses at most 2N BD ; 6 rank( ) lg(M=B) + 5 parallel I/Os, which asymptotically matches the lower bound and improves upon the BMMC algorithm in Cor93]. When rank( ) is low, this method is an improvement over the general-...

• Type: Conference
• Year: 1993
• Where: SPAA
• Authors: Thomas H. Cormen, Leonard F. Wisniewski
• Keywords: Bmmc Permutation, Distributed And Parallel Computing, Lower Bound, Parallel I/os, SPAA 1993