Random walks in peer-to-peer networks

Abstract

Abstract-We quantify the effectiveness of random walks for searching and construction of unstructured peer-to-peer (P2P) networks. For searching, we argue that random walks achieve improvement over flooding in the case of clustered overlay topologies and in the case of re-issuing the same request several times. For construction, we argue that an expander can be maintained dynamically with constant operations per addition. The key technical ingredient of our approach is a deep result of stochastic processes indicating that samples taken from consecutive steps of a random walk can achieve statistical properties similar to independent sampling (if the second eigenvalue of the transition matrix is bounded away from 1, which translates to good expansion of the network; such connectivity is desired, and believed to hold, in every reasonable network and network model). This property has been previously used in complexity theory for construction of pseudorandom number generators. We reveal another facet of this theory and translate savings in random bits to savings in processing overhead.

How to Explore a Fast-Changing World (Cover Time of a Simple Random Walk on Evolving Graphs)

“…In recent years, different authors have proposed the use of random walk for a large variety of tasks and networks; to name but a few: querying in sensor and ad-hoc networks [18,5,1], searching in peer-to-peer networks [12], gossiping [16], PageRank and search engines on the web [13].…”

The expansion and mixing time of skip graphs with applications

“…This can be used for a variety of applications such as load balancing, gathering statistics on the nodes of the skip graph and for finding highly replicated data items. It is known that in unstructured P2P systems, when the underlying graph expands there are algorithms for locating data items which are more efficient than simple flooding [6]. Furthermore, it was shown [11] that in some cases unstructured P2P systems can locate items faster than structured systems.…”

DANTE: A Self-adapting Peer-to-Peer System

“…Furthermore, it has been shown [7,8] that the sample obtained with this mechanism is a good sample of the overall network. Indeed, when the network has highly connected nodes or hubs (possibly due to low or medium loads), since the collecting message follows a random walk, these hubs will be reached with higher probability than poorly connected nodes.…”