Implicit data structures for fast search and update

AbstractWe 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 search. θ(N12) 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 the upper bound can be reduced to O(N13 log N) if arrangements other than fixed partial orders are used