Implicit data structures for weighted elements

Abstract

Several new data structures are presented for dictionaries containing elements with different weights (access probabilities). The structures use just one location in addition to those required for the values of the elements. The first structure supports a worst-case search time that is within a constant multiplicative factor of optimal, in terms of the rank of the weight of the desired element with respect to the multiset of weights. If the values of the elements that comprise the dictionary have been drawn from a uniform distribution, then a variation of this structure achieves average search times that are asymptotically very good. Similar results are established for data structures which handle the case in which the intervals between consecutive dictionary values also have access probabilities. Lower bounds are presented for the worst-case search complexity.