Abstract:
With the rise of dynamic reconfigurable networks such as Peer-to-Peer (P2P) networks, overlay networks, ad hoc wireless and mesh networks, it has become important to construct and maintain topologies with various desirable properties (such as connectivity, low diameter, expansion, low degree etc.) in an efficient decentralized manner. The main result of this paper is a distributed protocol called DConstructor that given any (connected) network topology will "converge" to a given (desired) target topology such as an expander, hypercube, or Chord, with high probability. Our protocol is efficient, lightweight, and scalable, and it incurs only O(polylog(n)) overhead (where n is the network size) for topology construction and maintenance: only polylogarithmic (in n) bits need to be processed and sent by each node per round, the convergence time is polylogarithmic rounds and any node’s computation cost per round is also polylogarithmic. Our protocol is robust and self-repairing in the sense that it will converge to the desired topology in polylogarithmic rounds and polylogarithmic communication cost under dynamic topology changes and arbitrary insertions and deletions of nodes.
