Parallel algorithms for red–black trees

Abstract

We present parallel algorithms for the following four operations on red–black trees: construction, search, insertion, and deletion. Our parallel algorithm for constructing a red–black tree from a sorted list of n items runs in O(1) time with n processors on the CRCW PRAM and runs in O(loglogn) time with n/loglogn processors on the EREW PRAM. Our construction algorithm does not require the assumptions that previous construction algorithms used. Each of our parallel algorithms for search, insertion, and deletion in red–black trees runs in O(logn+logk) time with k processors on the EREW PRAM, where k is the number of unsorted items to search for, insert, or delete and n is the number of nodes in a red–black tree.