A fast selection algorithm for meshes with multiple broadcasting

One of the fundamental algorithmic problems in computer science involves selecting the kth smallest element in a collection A of n elements. We propose an algorithm design methodology to solve the selection problem on meshes with multiple broadcasting. Our methodology leads to a selection algorithm that runs in O(n^1/8(log n)^3/4)) time on a mesh with multiple broadcasting of size n ^3/8(log n)^1/4×n^5/8/(log n)^1/4. This result is optimal over a large class of selection algorithms. Our result shows that just as for semigroup computations, selection can be done faster on suitably chosen rectangular meshes than on square meshes