Permutation algorithms on optical multi-trees

The Optical Multi-Trees (OMULT) is an interconnection network proposed by Sinha and Bandyopadhyay [B.P. Sinha, S. Bandyopadhyay, OMULT: An optical interconnection system for parallel computing, Lecture notes in Computer Science 3149 (2004) 302–312], for optoelectronic parallel computers. Various algorithms including matrix multiplication, DFT computation, sorting, prefix sum have been successfully mapped on this architecture. In this paper, we develop efficient parallel algorithms for some commonly used permutations namely, bit reversal, vector reversal, perfect shuffle, unshuffle and transpose on the OMULT network. Our algorithm for bit reversal permutation requires 8logn electronic moves +7 optical moves for n2 data elements and O(n) electronic moves +3 optical moves for n3 data elements; the vector reversal for n3 data elements requires 3g(n) electronic moves +4 optical moves, where g(n) is the time for local vector reversal on n data elements; the perfect shuffle for n3 data elements requires (3f(n)+8) electronic moves +8 optical moves, where f(n) is the time for local perfect shuffle on n data elements, and the transpose for n3 data elements runs in at most three optical moves, all using 2n3–n2 processors.