Optimal Routing in a Small-World Network

Recently a bulk of research [14, 5, 15, 9] has been done on the modelling of the smallworld phenomenon, which has been shown to be pervasive in social and nature networks, and engineering systems [16, 1, 2, 11]. In order to examine the navigating aspects of small-world graphs, Kleinberg [9] proposes a network model based on a d-dimensional torus lattice with longrange links chosen at random according to the d-harmonic distribution. Kleinberg shows that the greedy routing algorithm, by using only local information, performs in O(lg2 n) expected number of hops. We extend Kleinberg’s small-world model in that each node x has two more random links to nodes chosen uniformly and randomly within (lg n) 2 d Manhattan distance from x, where d denotes the dimension of the model. Based on this extended model, we then propose an oblivious algorithm that can route messages between any two nodes in O(lg n) expected number of hops, which is an optimal expected bound for routing. Our routing algori...

• Type: Conference
• Year: 2005
• Where: PDCAT
• Authors: Jianyang Zeng, Wen-Jing Hsu
• Keywords: Distributed And Parallel Computing, Kleinberg’s Small-world Model, PDCAT 2005, Routing Algorithm, Small-world Networks