A Parallel, In-Place, Rectangular Matrix Transpose Algorithm

This thesis presents a novel algorithm for Transposing Rectangular matrices In-place and in Parallel (TRIP) including a proof of correctness and an analysis of work, span and parallelism. After almost 60 years since its introduction, the problem of in-place rectangular matrix transposition still does not have a satisfying solution. Increased concurrency in todays computers, and the need for low-overhead algorithms to solve memory-intense challenges are motivating the development of algorithms like TRIP. The algorithm is based on recursive splitting of the matrix into sub-matrices, independent, parallel transposition of these sub-matrices, and subsequent combining of the results by a parallel, perfect shuffle. We prove correctness of the algorithm for different matrix shapes (ratios of dimensions), and analyze work and span: For an $M\times N$ matrix, where $M>N$, and both $M$ and $N$ are powers of two, TRIP has work \[W_1 \trip(M,N)=\Theta\left(MN\log\fracsubmitted by Stefan AmbergerUniversität Linz, Masterarbeit, 2019(VLID)353319