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(log log n) time with n/log log n 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(log n + log k) 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. © 2001 Elsevier Science B.V. All rights reserved.
Park, H., & Park, K. (2001). Parallel algorithms for red-black trees. Theoretical Computer Science, 262(1–2), 415–435. https://doi.org/10.1016/S0304-3975(00)00287-5