Implicit data structures (Preliminary Draft)

We consider representations of data structures in which the relative ordering of the values stored is implicit in the pattern in which the elements are retained, rather than explicit in pointers. Several implicit schemes for storing data are introduced to permit efficient implementation of the instructions insert, delete and find. &thgr;(@@@@N) basic operations are shown to be necessary and sufficient, in the worst case, to perform these instructions provided that the data elements are kept in some fixed partial order. We demonstrate, however, that further improvements can be made if an arrangement other than a fixed partial order is used. A structure, based on a fixed partial order, is introduced to facilitate multiple key searches. This structure, together with the retrieval scheme based upon it, is shown to be within a constant factor of the optimal one based on a partial order.