 
Summary: PREPRINT. Journal of Algorithms 29:256276, 1998.
Approximate indexed lists
Arne Andersson \Lambda Ola Petersson y
Abstract
Let the position of a list element in a list be the number of elements preceding it plus one.
An indexed list supports the following operations on a list: Insert; delete; return the position
of an element; and return the element at a certain position. The order in which the elements
appear in the list is completely determined by where the insertions take place; we do not require
the presence of any keys that induce the ordering.
We consider approximate indexed lists, and show that a tiny relaxation in precision of the
query operations allows a considerable improvement in time complexity. The new data structure
has applications in two other problems; namely, list labeling and subset rank.
1 Introduction
An indexed list [5] is a list abstract data type that supports the following operations:
Insert(x; y): Insert list element y immediately after list element x, which may be a list header;
Delete(x): Delete list element x;
Pos(x): Return the position of list element x, that is, one plus the number of list elements preced
ing x;
Rep(i): Return the list element at position i.
In the first three operations, a reference to the parameter x is provided, and so no searches
