Small-World Networks: From Theoretical Bounds to Practical Systems

Abstract. In small-world networks, each peer is connected to its closest neighbors in the network topology, as well as to additional long-range contact(s), also called shortcut(s). In 2000, Kleinberg provided asymptotic lower bounds on routing performances and showed that greedy routing in an n-peer small-world network performs in Ω(n 1 3 ) steps when the distance to shortcuts is chosen uniformly at random, and in Θ(log2 n) when the distance to shortcuts is chosen according to a harmonic distribution in a d-dimensional mesh. Yet, we observe through experimental results that peer to peer gossip-based protocols achieving smallworld topologies where shortcuts are randomly chosen, perform reasonably well in practice. Kleinberg results are relevant for extremely large systems while systems considered in practice are usually of smaller size (they are typically made up of less than one million of peers). This paper explores the impact of Kleinberg results in the context of practical systems...

• Type: Conference
• Year: 2007
• Where: OPODIS
• Authors: François Bonnet, Anne-Marie Kermarrec, Michel Raynal
• Keywords: Distributed And Parallel Computing, Kleinberg, OPODIS 2007, Routing Complexity, Small-world Networks