Abstract

We address the fundamental problem of permuting the elements of an array of n elements according to some given permutation. Our goal is to perform the permutation quickly using only a polylogarithmic number of bits of extra storage. The main result is an algorithm whose worst case running time is O(n log n) and that uses O(log n) additional log n-bit words of memory. A simpler method is presented for the case in which both the permutation and its inverse can be computed at (amortised) unit cost. This algorithm requires O(n log n) time and O(1) words in the worst case. These results are extended to the situation in which we are to apply a power of the permutation. A linear time, O(1) word method is presented for the special case in which the data values are all distinct and are either initially in sorted order or will be when permuted. 1.

Citations