Quasi-Kautz Digraphs for Peer-to-Peer Networks

The topological properties of peer-to-peer overlay networks are critical factors that dominate the performance of these systems. Several nonconstant and constant degree interconnection networks have been used as topologies of many peer-to-peer networks. The Kautz digraph is one of these topologies that have many desirable properties. Unlike interconnection networks, peer-to-peer networks need a topology with an arbitrary order and degree, but the Kautz digraph does not possess these properties. In this paper, we propose MOORE: the first effective and practical peer-to-peer network based on the quasi-Kautz digraph with O(log(d) n) diameter and constant degree under a dynamic environment. The diameter and average routing path length, respectively, are shorter than that of CAN, butterfly, and cube-connected cycle, and are close to that of the de Bruijn and Kautz digraphs. The message cost of node joining and departing operations are at most 2.5d log(d) n and (2.5d + 1) log(d) n, and only d and 2d nodes need to update their routing tables. MOORE can achieve optimal diameter, high performance, good connectivity, and low congestion, evaluated by formal proofs and simulations.