Balanced distributed search trees do not exist

Abstract

This paper is a first 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 satisfies a lower bound of Ω(√m) 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 satisfies 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(√m), we show the bound to be tight.