A Self-Stabilization Process for Small-World Networks

Small-world networks have received significant attention because of their potential as models for the interaction networks of complex systems. Specifically, neither random networks nor regular lattices seem to be an adequate framework within which to study real-world complex systems such as chemical-reaction networks, neural networks, food webs, social networks, scientific-collaboration networks, and computer networks. Small-world networks provide some desired properties like an expected polylogarithmic distance between two processes in the network, which allows routing in polylogarithmic hops by simple greedy routing, and robustness against attacks or failures. By these properties, small-world networks are possible solutions for large overlay networks comparable to structured overlay networks like CAN, Pastry, Chord, which also provide polylogarithmic routing, but due to their uniform structure, structured overlay networks are more vulnerable to attacks or failures. In this paper we bring together a randomized process converging to a small-world network and a self-stabilization process so that a small-world network is formed out of any weakly connected initial state. To the best of our knowledge this is the first distributed self-stabilization process for building a small-world network.