The Complexity of Routing Algorithm in Small-World Networks

Small-World networks have been an active and common topic in many disciplines, including the social and natural sciences. In order to understand the "Small-World phenomenon" deeply, Klein berg proposed an augmented graph model and demonstrated "six degrees of separation" from an algorithmic perspective. Since then, the Small-World model has been an important issue which has been studied deeply. Based on our understanding of Small-World networks, a very generic framework is proposed for analysis and systematic study of such models. Most of Small-World networks can be embedded in this uniform framework which provides some insight into Small-World networks. Based on this model, the complexity of routing algorithm in Small-World networks is systematically studied and can be specified in a uniform and clear way. The main merits of this framework lie in its generality and openness.