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 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 di erent because leaves can have di erent depth therefore any wave in a pipeline is highly irregular To solve this problem we de ne virtual plane waves allowing us to develop an EREW dictionary for k keys with k processors and time O logn log k Later on we generalize the sequential algorithms on brother trees presented by Ottmann and Wood in the same way