Asynchronous resource discovery

Consider a dynamic, large-scale communication infrastructure (e.g., the Internet) where nodes (e.g., in a peer to peer system) can communicate only with nodes whose id (e.g., IP address) are known to them. One of the basic building blocks of such a distributed system is resource discovery - efficiently discovering the ids of the nodes that currently exist in the system. We present both upper and lower bounds for the resource discovery problem. For the original problem raised by Harchol-Balter, Leighton, and Lewin [3] we present an Ω2(n log n) message complexity lower bound for asynchronous networks whose size is unknown. For this model, we give an asymptotically message optimal algorithm that improves the bit complexity of Kutten and Peleg [4]. When each node knows the size of its connected component, we provide a novel and highly efficient algorithm with near linear O(nα(n, n)) message complexity (where α is the inverse of Ackerman's function). In addition, we define and study the Ad-hoc Resource Discovery Problem, which is a practical relaxation of the original problem. Our algorithm for ad-hoc resource discovery has near linear O(nα(n, n)) message complexity. The algorithm efficiently deals with dynamic node additions to the system, thus addressing an open question of [3]. We present a Ω(nα(n, n)) lower bound for the Ad-hoc Resource Discovery Problem, showing that our algorithm is asymptotically message optimal.