Parallel dictionaries with local rules on AVL and brother trees

We present a set of local rules to deal with dictionaries. Their main advantage is that they can be scheduled in a highly synchronized way to get parallel dictionaries on AVL trees. Up to now trees used in massively parallel dictionaries needed to have all the leaves at the same depth, such as 2-3 trees. Therefore, it was possible (in insertions and deletions) the bottom-up reconstruction of the tree in a very regular fashion, as a pipeline of plane waves moving up. On AVL trees the situation looks different because leaves can have different depth, therefore any wave in a pipeline is highly irregular. To solve this problem we define virtual plane waves allowing us to develop an EREW dictionary for k keys with k processors and time O(log n + log k). Later on we generalize the sequential algorithms on brother trees presented by Ottmann and Wood in the same way. (C) 1998 Elsevier Science B.V. All rights reserved.