When Expanders Help Self-Healing Distributed R-Tree Overlays

We present the first self-healing architecture for recovering semantic DR-tree overlays in response to physical nodes failures (crash). Our work builds on two of our recent results: the overlay virtualization and churn tolerant design of constant expanders for distributed R-trees. That is, the proposed self-healing strategy, in order to recover the searchability and the semantic organization of the original overlay, exploits both the randomly uniform distribution of the logical nodes on top of the physical network and the additional virtual links of the expander. The convergence time of our scheme is O(log(n)) and the height of the recovered tree is increased only by Ω(log f) with respect to the original overlay (n is the size of the network and f are the number of crashed nodes). We validate our scheme via simulations including measures of the recovery time, the recovery extra cost and finally the impact of the recovery scheme on the distributed R-tree connectivity and semantics.