Fully Dynamic Balanced and Distributed Search Trees with Logarithmic Costs

In this paper we consider the dictionary problem in a message passing distributed environment. We introduce a new version of an order-preserving distributed search tree, called BDST for Balanced and Distributed Search Tree, capable to both grow and shrink as long as keys are inserted and deleted. This is the rst distributed data structure to explicitly support both insertion and deletion with logarithmic costs, i.e. a key can be searched, inserted and deleted in O(log n) messages, where n is the number of servers. Moreover a range query can be performed in O(logn + d k b e) messages, where k is the number of items returned by the search and b is the capacity of each server. Since balance is explicitly maintained, the structure is able to adapt itself to any input distribution and does not depend on any uniformity assumption to obtain logarithmic performances.