Parallel dynamic lowest common ancestors

Abstract

This paper gives a CREW PRAM algorithm for the problem of finding lowest common ancestors in a forest under the insertion of leaves and roots and the deletion of leaves. For a forest with a maximum of n vertices, the algorithm takes O(m/p + r log p + min(m,r log n)) time and O(n) space using p processors to process a sequence of m operations that are presented over r rounds. Furthermore, lowest common ancestor queries can be done in worst case constant time using a single processor. For one processor, the algorithm matches the bounds achieved by the best sequential algorithm known.