The Movement and Permutation of Columns in Magnetic Bubble Lattice Files

In this paper, we propose a layout of access channels in a new kind of magnetic bubble memory called a bubble lattice file. We further assume that interchange of bubble columns under certain channels is possible. We then propose an algorithm for moving a column to any other location using minimal number of column interchanges. The algorithm and the proof of its optimality involves signed-digit representation of numbers by a mixed radix system. Based on this, we next propose a simple algorithm to permute a set of columns. Analysis of this algorithm for both the worst and average case is given. The algorithm is shown to be close to optimal for both cases. Finally, based on an optimization consideration, a geometric layout of access channels is suggested for the best performance of the proposed algorithm.