This paper addresses the fundamental problem of permuting the elements of an array of n elements according to some given permutation. It aims to perform the permutation quickly by 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 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 a power of the permutation must be applied. 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.

The fundamental problem of permuting the elements of an array according to some given permutation is addressed. The goal is to perform the permutation quickly using only a polylogarithmic number of bits of extra storage. The main result is an O(n log n)-time, O(log/sup 2/n)-space worst case method. A simpler method is presented for the case in which both the permutation and its inverse can be computed at (amortized) unit cost. This algorithm requires O(n log n) time and O(log n) bits in the worst case. These results are extended to the situation in which a power of the permutation is to be applied. A linear time, O(log n)-bit 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.>

We develop a method of representing binary search trees in an environment in which pointers and other structural information may be "lost" or "maliciously altered". Our fault tolerant representation permits any 2 field changes to be detected and any 1 to be corrected without significantly increasing to storage requirements of the binary tree. The detection and correction procedures applied to the entire tree require 0(n) time.Our discipline is also used to represent binary search trees with a single pointer per datum without altering the cost of searching or updating. While our scheme can be applied in conjunction with any underlying tree balancing scheme ([AVL], bounded balance [Nievergelt et al] etc), if no balancing scheme is employed, the trees we form will have significantly shorter search paths than those formed using the straightforward algorithm.