Multiple Random Walks to Uncover Short Paths in Power Law Networks

TL;DR

This paper explores how multiple random walks can efficiently uncover short paths in large power law networks, even without full topology knowledge, by leveraging their edge coverage and crossing properties.

Contribution

It demonstrates that random walks can find short paths in power law networks through their edge coverage and crossing probabilities, independent of the paths taken.

Findings

Random walks observe a large fraction of network edges.

Paths of random walks cross with high probability after visiting few nodes.

Simulation results confirm effectiveness on real-world networks.

Abstract

Consider the following routing problem in the context of a large scale network $G$, with particular interest paid to power law networks, although our results do not assume a particular degree distribution. A small number of nodes want to exchange messages and are looking for short paths on $G$. These nodes do not have access to the topology of $G$ but are allowed to crawl the network within a limited budget. Only crawlers whose sample 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 the ability of RWs to find short paths bears no relation to the paths that they take. Instead, it relies on two properties of RWs on power law networks: 1) RW's ability observe a sizable fraction of the network edges; and 2) an almost 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.