Parallel selection algorithms with analysis on clusters

We present three deterministic parallel selection algorithms with analysis on clusters. The first and second algorithms are proposed on the CGM (Coarse Grained Multicomputer) model. The first algorithm achieves optimality with respect to its computation time and runs in O(n/p) computation time and O(min(log p, log log n)) communication rounds if n/p⩾p^ε for any ε>0, where n is the number of input elements and p is the number of processors. The second algorithm achieves optimality with respect to the number of communication rounds and runs in O(n/p log p) computation time and the constant number of communication rounds if n/p>p^ε for any ε>0. The third selection algorithm is a hybrid algorithm of the above two algorithms and suitable for practical cluster computing. The algorithms are implemented using PVM, and its experimental results are also presented