HRing: A Structured P2P Overlay Based on Harmonic Series

This paper presents Harmonic Ring (HRing), a structured peer-to-peer (P2P) overlay where long links are built along the ring with decreasing probabilities coinciding with the Harmonic Series. HRing constructs routing tables based on the distance between node positions instead of node IDs in order to eliminate the effect of node ID distribution on the long link distribution and load balance. It supports leave-and-rejoin load balance without incurring uneven long link distribution. In addition, node IDs can be any form, like number, string, address, and date, without the prerequisite of uniform distribution, so they can preserve the semantics and range locality of data objects. HRing supports multidimensional range queries. Each node is expected to have O(ln(n)) long links. The construction of O(ln(n)) long links for a node costs (O(ln(n)) messages. Routing queries achieve O(ln(n)) hops. Analyses and simulations demonstrate the efficiency of query routing and the effectiveness of the long link construction method.