An Analysis Framework for Distributed Hierarchical Directories

We provide a novel analysis framework for distributed hierarchical directories for an arbitrary set of dynamic (online) requests. We prove a general \({\cal O}(\eta\cdot \varphi \cdot \sigma^3 \cdot h)\) competitive ratio for any distributed hierarchical directory, where η is a write set size related parameter, ϕ and σ are stretch and growth related parameters, and h is the number of levels in the hierarchy. Through this framework, we give bounds for several known distributed directory protocols. In general network topologies, we obtain \({\cal O}(\log^2 n\cdot\log D)\) competitive ratio, where n and D are the number of nodes and the diameter, respectively, of the network. Moreover, we obtain \({\cal O}(\log D)\) competitive ratio in constant-doubling metric topologies. To the best of our knowledge, this is the first (competitive) dynamic analysis for distributed hierarchical directories.