Graph-Theoretic Analysis of Kautz Topology and DHT Schemes

Many proposed distributed hash table (DHT) schemes for peer-to-peer network are based on some traditional parallel interconnection topologies. In this paper, we show that the Kautz graph is a very good static topology to construct DHT schemes. We demonstrate the optimal diameter and optimal fault tolerance properties of the Kautz graph and prove that the Kautz graph is (1+o(1))-congestion-free when using the long path routing algorithm. Then we propose FissionE, a novel DHT scheme based on Kautz graph. FissionE is a constant degree, O(log N) diameter and (1+o(1))-congestion-free. FissionE shows that the DHT scheme with constant degree and constant congestion can achieve O(log N) diameter, which is better than the lower bound Ω(N 1/d) conjectured before.

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