Parallel dictionaries with local rules on AVL and brother trees

Abstract

We present a set of local rules to deal with dictionaries, having as a main advantage their possible scheduling in a highly synchronized way to get parallel dictionaries on AVLs. 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 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 {\it 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 se