Distributed construction of a fault-tolerant network from a tree

We present an algorithm by which nodes arranged in a tree, with each node initially knowing only its parent and children, can construct a fault-tolerant communication structure (an expander graph) among themselves in a distributed and scalable way. The tree overlayed with this logical expander is a useful structure for distributed applications that require the intrinsic "treeness" from the topology but cannot afford any obstruction in communication due to failures. At the core of our construction is a novel distributed mechanism that samples nodes uniformly at random from the tree. In the event of node joins, node departures or node failures, the expander maintains its own fault tolerance and permits the reformation of the tree. We present simulation results to quantify the convergence of our algorithm to a fault tolerant network having both good vertex connectivity and expansion properties.