Fast parallel permutation algorithms

We investigate the problem of permuting n data items on an EREW PRAM with p processors using little additional storage. We present a simple algorithm with run time O((n/p)log n) and an improved algorithm with run time O(n/p+log nloglog(n/p)). Both algorithms require n additional global bits and O(1) local storage per processor. If prefix summation is supported at the instruction level, the run time of the improved algorithm is O(n/p). The algorithms can be used to rehash the address space of a PRAM emulation