Availability models for underlay aware overlay networks

Event broker networks are P2P overlays constructed out of a few select nodes of the underlying physical network (aka underlay). Reliable event delivery on such networks requires the overlay to be highly available. While high availability is usually achieved by redundant paths between the rendezvous node and the subscriber, redundancy at the overlay level alone is insufficient to guarantee availability - redundant paths in the overlay have to correspond to node disjoint paths in the underlay network for true availability. In this paper, we propose two models of availability. In the Manifest Availability model, distinct paths at the overlay level are node disjoint at the underlay as well - this is a strong availability condition. We can weaken this to the Latent Availability model where it is only guaranteed that any two overlay nodes have a guaranteed number of node disjoint paths between them in the underlay. We analyze both the models for complexity of formation and maintenance, and prove that in the general case, both are NP-complete. We then identify a set of practical constraints applicable to large scale networks. We demonstrate that under these constraints, constructing latent availability overlays reduces to a polynomial time problem. We also introduce the concept of reduced underlays, and further reduce the complexity of the problem of determining latent availability overlays.