Randomized Sorting and Selection on Mesh-Connected Processor Arrays

We show that sorting an input of size N = n superscript 2 can be performed by an n X n mesh-connected processor array in 2.5n +0(n) parallel communication steps and using constant size queues, with high probability. The best previously known algorithm for this problem required 3n + 0(n) steps. We also show that selecting the element of rank k out of N = n superscript 2 inputs on an n X n mesh can be performed in 1.25n + 0(n) steps and using constant size queues, with high probability. The best previously known algorithm for this problem involved sorting, and required 3n + 0(n) steps. Both of our algorithms can be generalized to higher dimensions, achieving bounds better than the known results. 1Aike