Searching in a Sorted Linked List

Abstract

Let A be the array of n integers in {0, 1, …, n-1}. A tree is constructed in O(nloglogm/p+loglogm) time with p processors based on the trie with all the given integers. Additional nodes (O(nloglogm) of them) are added to the tree. After the tree is construct we can, for any given integer, find the predecessor and successor of this integer, insert or delete the integer in A in O(loglogm) time. This result demonstrates for the searching purpose we need not to sort the input numbers into a sorted array for this would need at least O(logn/loglogn) time while this algorithm for constructing the tree can run in O(loglogm) time with n processors.