Cayley DHTs - A Group-Theoretic Framework for Analyzing DHTs Based on Cayley Graphs

Static DHT topologies influence important features of such DHTs such as scalability, communication load balanc- ing, routing efficiency and fault tolerance. Nevertheless, it is commonly recognized that the primary difficulty in design- ing DHT is not in static DHT topologies, but in the dynamic DHT algorithm which adapts various static DHT topolo- gies to a dynamic network at Internet. As a direct conse- quence, the DHT community has been paying more atten- tion to the dynamic DHT algorithm design, resulting in a variety of DHT systems lacking of a common view for anal- ysis and interoperation.In this paper we reiterate the im- portance of static DHT topologies in the DHT system de- sign by analyzing and classifying current DHTs in terms of their static topologies based on a grouptheoretic model: Cayley graphs. We show that most of current DHT propos- als use Cayley graphs as static DHT topologies, thus tak- ing advantage of several important Cayley graph proper- ties such as vertex/edge symmetry, decomposability, opti- mal fault tolerance and hamiltonicity. We observe that sev- eral non-Cayley-graph based DHT proposals such as Ko- orde/D2B/Distance Halving and Pastry/Tapestry also rely on techniques in their dynamic DHT algorithm design try- ing to imitate desirable Cayley graph properties. Based on Cayley graphs, we propose the class of Cayley DHTs as a unified group-theoretic model for investigating DHTs from a graph theoretic perspective. The significance of Cayley DHTs is in their explicit inspiration to a uniform dynamic DHT algorithm design, which can directly leverage alge- braic design methods thus is able to generate sets of high- performance DHTs adopting various Cayley graph based static DHT topologies but still sharing the same dynamic DHT algorithm.