Asynchronous resource discovery

Abstract

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 [M. Harchol-Balter, T. Leighton, D. Lewin, Resource discovery in distributed networks, in: Proceedings of the Eighteenth Annual ACM Symposium on Principles of Distributed Computing, ACM Press, 1999, pp. 229–237] we present an Ω( 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 [S. Kutten, D. Peleg. Asynchronous resource discovery in peer-to-peer networks, in: Proceedings of the 21st IEEE Symposium on Reliable Distributed Systems (SRDS’02), 2002, p. 224]. 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 [M. Harchol-Balter, T. Leighton, D. Lewin, Resource discovery in distributed networks, in: Proceedings of the Eighteenth Annual ACM Symposium on Principles of Distributed Computing, ACM Press, 1999, pp. 229–237]. We show a reduction from the classic Union-Find problem proving a Ω( nα( n, n)) lower bound for the Ad-hoc Resource Discovery Problem. Thus our Ad-hoc Resource Discovery algorithm is asymptotically message optimal.