Abstract:
Abstract — We quantify the effectiveness of random walks for searching and construction of unstructured peer-to-peer (P2P) networks. We have identified two cases where the use of random walks for searching achieves better results than flooding: a) when the overlay topology is clustered, and b) when a client re-issues the same query while its horizon does not change much. 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.
Citations
|
1294
|
The Probabilistic Method
– Alon, Spencer
- 1993
|
|
983
|
An Introduction to Probability Theory and Its Application”, volume 2, two editions
– Feller
|
|
759
|
The algebraic eigenvalue problem
– Wilkinson
- 1965
|
|
702
|
On power-law relationships of the internet topology
– Faloutsos, Faloutsos, et al.
- 1999
|
|
637
|
Emergence of scaling in random networks
– Barabasi, Albert
- 1999
|
|
300
|
Search and replication in unstructured peer-to-peer networks
– Lv, Cao, et al.
- 2002
|
|
233
|
Inferring web communities from link topology
– Gibson, Kleinberg, et al.
- 1998
|
|
207
|
Trawling the Web for emerging cyber-communities
– Kumar, Raghavan, et al.
- 1999
|
|
197
|
Making Gnutella-like P2P Systems Scalable
– Chawathe, Ratnasamy, et al.
- 2003
|
|
192
|
Peer-to-Peer: Harnessing the Power of Disruptive Technologies
– Oram, Minar, et al.
- 2001
|
|
167
|
How to recycle random bits
– Impagliazzo, Zuckerman
- 1989
|
|
158
|
Reversible markov chains and random walks on graphs. monograph in preparation. [Online]. Available: http://stat-www.berkeley.edu/users/aldous/RWG/book.html
– Aldous, Fill
|
|
143
|
Algorithms for random generation and counting: A markov chain approach
– Sinclair
- 1993
|
|
109
|
On distinguishing between internet power law topology generators
– Bu, Towsley
- 2002
|
|
88
|
Deterministic Simulation in LogSpace
– Ajtai, Komlos, et al.
- 1987
|
|
84
|
Building low-diameter p2p networks
– Pandurangan, Raghavan, et al.
|
|
63
|
Explicit constructions of linear-sized superconcentrators
– Gabber, Galil
- 1981
|
|
61
|
On the Markov chain simulation method for uniform combinatorial distributions and simulated annealing", Probability in
– Aldous
- 1987
|
|
59
|
Deconstructing the Kazaa Network
– Leibowitz, Ripeanu, et al.
- 2003
|
|
51
|
A chernoff bound for random walks on expander graphs
– Gillman
- 1993
|
|
39
|
Spectral analysis of internet topologies
– Gkantsidis, Mihail, et al.
- 2003
|
|
34
|
Spectra of random graphs with given expected degrees
– CHUNG, LU, et al.
|
|
33
|
Modeling peer-to-peer network topologies through “small-world” models and power laws
– Jovanović, Annexstein, et al.
- 2001
|
|
30
|
Bounds on the cover time
– Broder, Karlin
- 1989
|
|
30
|
On certain connectivity properties of the internet topology
– Mihail, Papadimitriou, et al.
- 2003
|
|
27
|
Conductance and Congestion in Power Law Graphs
– Gkantsidis, Mihail, et al.
- 2003
|
|
3
|
and Kai-Yeung Siu, “Distributed construction of random expander networks
– Law
- 2003
|
|
3
|
Snapshots of the gnutella network,” http://crawler.limewire.org/data.html
– org
- 2002
|
