Balanced Distributed Search Trees Do Not Exist

This paper is a rst step towards an understanding of the inherent limitations of distributed data structures. We propose a model of distributed search trees that is based on few natural assumptions. We prove that any class of trees within our model satis es a lower bound of (pm) on the worst case height of distributed search trees for m keys. That is, unlike in the single site case, balance in the sense that the tree height satis es a logarithmic upper bound cannot be achieved. This is true although each node is allowed to have arbitrary degree (note that in this case, the height of a single site search tree is trivially bounded by one). By proposing a method that generates trees of height O(pm), we show the bound to be tight.