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 2
d
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.