Abstract
We show that n integers in {0, 1, …, m-1} can be sorted into a linked list in constant time using nlogm processors on the Priority CRCW PRAM model, and they can be sorted into a linked list in O(loglogm/logt) time using nt processors on the Priority CRCW PRAM model.
Highlights
It is well known that is a time lower bound for sorting integers
It is known that n integers in {0, 1, ..., m-1} can be sorted into a linked list in O(loglogm) time using n processors on the CRCW PRAM
In this paper we show that n integers in {0, 1, ..., m-1} can be sorted into a linked list in constant time using nlogm processors on the Priority CRCW PRAM model, and they can be sorted into a linked list in O(loglogm/logt) time using nt processors on the Priority CRCW PRAM model
Summary
It is well known that (logn/loglogn) is a time lower bound for sorting integers For leaf a to find the lowest ancestor in the tree that has a left child which is not an ancestor of a, we will use the logm processors for a, if a’s ancestor at level l in trie is not a node in the tree (i.e. it has one child) processor l will write logm+1 into array B[l]. If leaf a locates b as the lowest ancestor in the tree that has a right child which is not an ancestor of a and a’ locates b as the lowest ancestor in the tree that has a left child which is not an ancestor of a’’ we link a to a’ This builds the linked list for the input integers in constant time. Theorem 1: n integers in {0, 1, ..., m-1} can be sorted into a linked list in constant time with nlogm processors on the Priority CRCW PRAM. 2018) that the tree built here can be augmented to facilitate predecessor and successor queries and insertion in O (loglogm) time
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