. 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. The new algorithm is somewhat simpler and has smaller constants in the time and space complexity. 1 Introduction Finding lowest common ancestors in trees is a frequently occurring problem in the literature and has found application in such diverse problems as computing dominators in reducible flow graphs [1], detecting negative cycles in sparse graphs [12], planarity testing [9], and computing weighted matc...

Contents 1 Introduction 3 2 Models of computation 6 3 The Set Union Problem 9 4 The Worst--Case Time Complexity of a Single Operation 15 5 The Set Union Problem with Deunions 18 6 Split and the Set Union Problem on Intervals 22 7 The Set Union Problem with Unlimited Backtracking 26 1 Introduction An equivalence relation on a finite set S is a binary relation that is reflexive symmetric and transitive. That is, for s; t and u in S, we have that sRs, if sRt then tRs, and if sRt and tRu then sRu. Set S is partitioned by R into equivalence classes where each class cointains all and only the elements that obey R pairwise. Many computational problems involve representing, modifying and tracking the evolution of equivalenc

This paper presents a system to find automatically words from a definition or a paraphrase. The system uses a lexical database of French words that is comparable in its size to WordNet and an algorithm that evaluates distances in the semantic graph between hypernyms and hyponyms of the words in the definition. The paper first outlines the structure of the lexical network on which the method is based. It then describes the algorithm. Finally, it concludes with examples of results we have obtained.