Localized search in sorted lists

It is well known that every one of the set operations <underline>insert, delete</underline> and <underline>member</underline> can be performed in O(log n) steps, where n is the number of elements currently in the set. Here we implement these operations and a <underline>move</underline> operation for a sorted list with f fingers (points of reference) established on the list. It is shown that these operations can be performed in O(log d) steps, where d is the distance between the corresponding finger and the key involved.