Spartan: Sparse Robust Addressable Networks

We present an overlay design called Sparse Robust Addressable Network (Spartan) that can tolerate heavy adversarial churn. We show that Spartan can be built efficiently in a fully distributed manner within $O(\log n)$ rounds. Furthermore, the Spartan overlay structure can be maintained, again, in a fully distributed manner despite adversarially controlled churn (i.e., nodes joining and leaving) and significant variation in the number of nodes. When the number of nodes in the network lies in $[n, fn]$ for any fixed $f\ge 1$ the adversary can remove up to $\epsilon n$ nodes and add up to $\epsilon n$ nodes (for some small but fixed $\epsilon > 0$) within {\em any} period of $P$ rounds for some $P \in O(\log \log n)$. Moreover, the adversary can add or remove nodes from the network at will and without any forewarning. Despite such uncertainty in the network, Spartan maintains $\Theta(n/\log n)$ committees that are stable and addressable collections of $\Theta(\log n)$ nodes each. Any node that enters the network will be able to gain membership in one of these committees within $O(1)$ rounds. The committees are also capable of performing sustained computation and passing messages between each other. Thus, any protocol designed for static networks can be simulated on Spartan with minimal overhead. This makes Spartan an ideal platform for developing applications. All our results hold with high probability.