Random walks in peer-to-peer networks: Algorithms and evaluation

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. Related to the simulation of random walks is also the distributed computation of aggregates, such as averaging. 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 on an expander graph can achieve statistical properties similar to independent sampling. 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.

[1]  Scott Shenker,et al.  Making gnutella-like P2P systems scalable , 2003, SIGCOMM '03.

[2]  Zvi Galil,et al.  Explicit Constructions of Linear-Sized Superconcentrators , 1981, J. Comput. Syst. Sci..

[3]  David Kempe,et al.  A decentralized algorithm for spectral analysis , 2004, STOC '04.

[4]  Zvi Galil,et al.  Proceedings of the 30th IEEE symposium on Foundations of computer science , 1994, FOCS 1994.

[5]  P. Oscar Boykin,et al.  Scalable Percolation Search in Power Law Networks , 2004, ArXiv.

[6]  Russ Bubley,et al.  Randomized algorithms , 1995, CSUR.

[7]  M. Jovanovi.  MODELING PEER-TO-PEER NETWORK TOPOLOGIES THROUGH “ SMALL-WORLD ” MODELS AND POWER LAWS , 2001 .

[8]  D. Aldous.  On the Markov Chain Simulation Method for Uniform Combinatorial Distributions and Simulated Annealing , 1987, Probability in the Engineering and Informational Sciences.

[9]  Donald F. Towsley,et al.  On distinguishing between Internet power law topology generators , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[10]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[11]  Christos Gkantsidis,et al.  Hybrid search schemes for unstructured peer-to-peer networks , 2005, Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies..

[12]  Christos Gkantsidis,et al.  Spectral analysis of Internet topologies , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[13]  Anna R. Karlin,et al.  Bounds on the cover time , 1989 .

[14]  Johannes Gehrke,et al.  Gossip-based computation of aggregate information , 2003, 44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings..

[15]  Andrei Z. Broder,et al.  Graph structure in the Web , 2000, Comput. Networks.

[16]  Fan Chung Graham,et al.  The Spectra of Random Graphs with Given Expected Degrees , 2004, Internet Math..

[17]  Adam Wierzbicki,et al.  Deconstructing the Kazaa network , 2003, Proceedings the Third IEEE Workshop on Internet Applications. WIAPP 2003.

[18]  R. F. Brown,et al.  PERFORMANCE EVALUATION , 2019, ISO 22301:2019 and business continuity management – Understand how to plan, implement and enhance a business continuity management system (BCMS).

[19]  James F. Doyle,et al.  Peer-to-Peer: harnessing the power of disruptive technologies , 2001, UBIQ.

[20]  J. H. Wilkinson.  The algebraic eigenvalue problem , 1966 .

[21]  Russell Impagliazzo,et al.  How to recycle random bits , 1989, 30th Annual Symposium on Foundations of Computer Science.

[22]  M -.  Estimating Aggregates on a Peer-to-Peer Network , 2003 .

[23]  Amin Saberi,et al.  Random Walks with Lookahead on Power Law Random Graphs , 2006, Internet Math..

[24]  Alistair Sinclair,et al.  Algorithms for Random Generation and Counting: A Markov Chain Approach , 1993, Progress in Theoretical Computer Science.

[25]  Michalis Faloutsos,et al.  On power-law relationships of the Internet topology , 1999, SIGCOMM '99.

[26]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[27]  Kai-Yeung Siu,et al.  Distributed construction of random expander networks , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[28]  Eli Upfal,et al.  Building low-diameter P2P networks , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.

[29]  Hector Garcia-Molina,et al.  Peer-to-peer research at Stanford , 2003, SGMD.

[30]  Andy Oram,et al.  Peer-to-Peer: Harnessing the Power of Disruptive Technologies , 2001 .

[31]  Jon M. Kleinberg,et al.  Inferring Web communities from link topology , 1998, HYPERTEXT '98.

[32]  Christos Gkantsidis,et al.  Conductance and congestion in power law graphs , 2003, SIGMETRICS '03.

[33]  Feller William,et al.  An Introduction To Probability Theory And Its Applications , 1950 .

[34]  Edith Cohen,et al.  Search and replication in unstructured peer-to-peer networks , 2002, ICS '02.

[35]  Ravi Kumar,et al.  Trawling the Web for Emerging Cyber-Communities , 1999, Comput. Networks.

[36]  Lada A. Adamic,et al.  Search in Power-Law Networks , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[37]  János Komlós,et al.  Deterministic simulation in LOGSPACE , 1987, STOC.

[38]  Amin Saberi,et al.  On certain connectivity properties of the Internet topology , 2003, 44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings..

[39]  Ravi Kumar,et al.  Self-similarity in the web , 2001, TOIT.

[40]  Noga Alon,et al.  The Probabilistic Method , 2015, Fundamentals of Ramsey Theory.

[41]  Stephen P. Boyd,et al.  Fastest Mixing Markov Chain on a Graph , 2004, SIAM Rev..

[42]  David J. Aldous,et al.  Lower bounds for covering times for reversible Markov chains and random walks on graphs , 1989 .

[43]  F. Chung,et al.  Spectra of random graphs with given expected degrees , 2003, Proceedings of the National Academy of Sciences of the United States of America.