Multiple Random Walks to Uncover Short Paths in Power Law Networks

Developing simple distributed algorithms to allow nodes to perform topology discovery and message routing using incomplete topological information is a problem of great interest in network science. Consider the following routing problem in the context of a large power law network G. A small number of nodes want to exchange messages over short paths on G. These nodes do not have access to the topology of G but are allowed to crawl the network subject to a budget constraint. Only crawlers whose paths cross are allowed to exchange topological information. In this work we study the use of random walks (RWs) to crawl G. We show that RWs have the ability to find short paths and that this bears no relation to the paths that they take. Instead, it relies on two properties of RWs on power law networks: The RW ability to observe a sizable fraction of the network edges; The near certainty that two distinct RW sample paths cross after a small percentage of the nodes have been visited. We show promising simulation results on several real world networks.