Searching in a Sorted Linked List and Sort Integers into a Linked List

Abstract

The research work consists of two parts. Part one is about Searching for an integer in a sorted Linked list. 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 constructed, for any given integer we can find the predecessor and successor of the integer, insert or delete the integer in O(loglogm) time. The 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.

Part two is on sorting integers into a linked list. There are various best algorithms for sorting integers. The current research work applies the recent important results of sorting integers in Ω(logn/loglogn) time. This algorithm takes “constant time” to sort integers into a linked list with nlogm processors and O(loglogm/logt) time using nt processors on the Priority CRCW PRAM model.