A Tree Storage Scheme for Magnetic Bubble Memories

In this paper, we study the problem of maintaining a file in magnetic bubble memories. A memory structure with a special loop ordering scheme is proposed, in which records are stored in a balanced tree form. Algorithms for searching, insertion, and deletion are proposed. They have the property that, after each operation, the file is restored to a balanced tree form. The searching operation takes time log22 n/(2 log2 log2 n) + O(log2 n) where n is the number of records in the file, while insertion and deletion take additional log2 n + O(1) time each. This scheme, however, requires that each switch be individually settable. In the latter part of the paper, the memory is slightly modified, and a new loop ordering scheme proposed. With only two control operations, we show that searching, insertion, and deletion of records in the tree can still be done although the tree can no longer be kept in balanced form. If the tree is balanced, then searching, insertion, and deletion take only 5/2 log2 (n + 1) + O(1) time each.