Parallel Dictionaries Using AVL Trees

AVL (Adel\u27son-Vel\u27skii and Landis) trees are efficient data structures for implementing dictionaries. We present a parallel dictionary, using AVL trees, on the EREW PRAM by proposing optimal algorithms to performkoperations withp(1 ≤p≤k) processors. An explicit processor scheduling is devised to avoid simultaneous reads in our parallel algorithm to performksearches, which avoids the need for any additional memory in the parallelization. To perform multiple insertions and deletions, we identify rotations (in addition to AVL tree rotations) required to restore balance and present parallel algorithms to performpinsertions/deletions inO(logn+ logp) time withpprocessors. © 1998 Academic Press