Lower Bound on de Bruijn Graphs Out-degree for Lower Traffic Load in Peer-to-peer Networks

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Designers search for N-nodes peer-to-peer networks that can have O(1) out-degree with O(log2 N) average distance.Peer-to-peer schemes based on de Bruijn graphs are found to meet this requirement. By defining average load to evaluate the traffic load in a network, we show that in order to decrease the average load, the average distance of a network should decrease while the out-degree should increase.Especially, given out-degree k and N nodes, peer-to-peer schemes based on de Bruijn graphs have lower average load than other existing systems. The out-degree k of de Bruijn graphs should not be O(1) but should satisfy a lower bound described by an inequality kk≥ N2, to ensure that the average load in peer-to-peer schemes based on de Bruijn graphs will not exceed that in Chord system.
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