On the Complexity of Permuting Records in Magnetic Bubble Memory Systems

In this paper we study the problem of permuting records in various simple models of magnetic bubble memories. Previous studies usually assumed the memory system either had one switch or n independently controlled switches, where n is the number of records to be permuted. In the former case, the time complexity to permute a set of n records is O(n
²
), while in the latter case, the time complexity is O(n). In this paper, we propose several simple models of bubble memory systems with their numbers of switches ranging between 1 and n and analyze the respective time complexities and respective numbers of control states for some permutation algorithms designed especially for them. Specifically, four models are studied: They have essentially log
2
n, 2√n, (log
2
n - log
2
log
2
n)
²
, and k switches; their respective time complexities are essentially (3/2)n log
2
n, (5/2)n, (7/2)n, and 2
^−1/k
kn
^1+(1/k)
; and their respective numbers of control states are essentially 4 log
2
n, 2
^√n+1
, 2n/log
2
n, and 4k.