Moore: An Extendable Peer-to-Peer Network Based on Incomplete Kautz Digraph with Constant Degree

The topological properties of peer-to-peer overlay networks are critical factors that dominate the performance of these systems. Several non-constant and constant degree interconnection networks have been used as topologies of many peer-to-peer networks. One of these has many desirable properties: the Kautz digraph. Unlike interconnection networks, peer-to-peer networks need a topology with an arbitrary size and degree, but the complete 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 incomplete Kautz digraph with O(log _d N) diameter and constant degree under a dynamic environment. The diameter and average routing path length are [log _d (N) - log _d (1 + 1/d)] and log _d N, respectively, and are shorter than that of CAN, butterfly, and cube-connected-cycle. They are close to that of complete de Bruijn and Kautz digraphs. The message cost of node joining and departing operations are at most 2.5 d log _d N and (2.5 d + 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.