Probabilistic Searching in Sorted Linked Lists

Abstract

Janko [2] and Bentley, Stanat, and Steele [1] have described probabilistic procedures for data manipulation in sorted linnked lists. Their procedures are based on an algorithm which performs a Member search operation using 2N^1/2 + O(1) expected steps where N is the number of elements in the list. In addition, Bentley, Stanat and Steele have shown that every Member search algorithm requires (2N)^1/2 + Ω(!) expected steps. In this paper, we improve the lower bound result in order to prove that the known algorithm for Member search is optimal.