Efficient scalable mesh algorithms for merging, sorting and selection

Efficient scalable algorithms are developed for a mesh with fixed buses. The problems considered are merging, sorting and selection. The size of the input is fixed at n, and the mesh size is varied from √n×√n to n×n. The merging algorithm is optimal for all the mesh sizes, whereas the sorting and selection algorithms are within factors of i/(1-ε) and log^4/3 n respectively, of the optimal