Massively parallel and distributed dictionaries on AVL and brother trees

Abstract

We present a set of local rules to deal with distributed dictionaries, having as a main advantage their possible scheduling in a highly synchronized way to get massively parallel dictionaries on AVLs. Recall that, 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) to reconstruct the tree bottom-up in a very regular fashion, as a pipeline of straight plane waves moving up. On AVL trees the situation looks different because leaves can have different depth, therefore any weave 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 T. Ottmann and D. Wood in the same way.