A Probabilistic Pipeline Algorithm for K Selection on the Tree Machine

We consider the problem of selecting the kth largest of n inputs, where initially the inputs are stored in the n leaf processors of the 2n − 1 processor tree machine. A probabilistic algorithm is presented that implements a type of pipelining to solve the problem in a simple data driven fashion, with each processor maintaining just a constant amount of state information. On any problem instance, the algorithm's running time is ²
n]/[loglog n], for some constant c > 0, with overwhelming probability.