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 O (η · φ · σ³ · 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 O (log² n · log D) competitive ratio, where n and D are the number of nodes and the diameter, respectively, of the network. Moreover, we obtain 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.