Matrix transpose on meshes with wormhole and XY routing

We give nearly optimal algorithms for matrix transpose on meshes with wormhole and XY routing and with a 1-port or 2-port communication model. For an N×N mesh, where N=3·2ⁿ and each mesh node has a submatrix of size m to be transposed, our algorithms take Nm/2 time steps for 1-port model, and about Nm/3.27 time steps for 2-port model. The lower bound is Nm/3.414. While there is no previously known algorithm for matrix transpose on meshes with wormhole and XY routing, a naive algorithm, which is naturally adapted from the well-known Recursive Exchange Algorithm, has a complexity of about Nm. That is our best algorithm improves over the naive algorithm by about a factor of 3.27, and is about a factor of 3.414/3.27 of the lower bound