Subscribe

Issue No.04 - April (2009 vol.8)

pp: 500-513

Roberto Beraldi , University of Rome, Rome

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TMC.2008.151

ABSTRACT

A recurrent problem when designing distributed applications is to search for a node with known property. File searching in peer-to-peer (P2P) applications, resource discovery in service-oriented architectures (SOAs), and path discovery in routing can all be cast as a search problem. Random walk-based search algorithms are often suggested for tackling the search problem, especially in very dynamic systems-like mobile wireless networks. The cost and the effectiveness of a random walk-based search algorithm are measured by the excepted number of transmissions required before hitting the target. Hence, to have a low hitting time is a critical goal. This paper studies the effect of biasing random walk toward the target on the hitting time. For a walk running over a network with uniform node distribution, a simple upper bound that connects the hitting time to the bias level is obtained. The key result is that even a modest bias level is able to reduce the hitting time significantly. This paper also proposes a search protocol for mobile wireless networks, whose results are interpreted in the light of the theoretical study. The proposed solution is for unstructured wireless mobile networks.

INDEX TERMS

Algorithm/protocol design and analysis, random walks, mobile ad hoc networks, search algorithms.

CITATION

Roberto Beraldi, "Biased Random Walks in Uniform Wireless Networks",

*IEEE Transactions on Mobile Computing*, vol.8, no. 4, pp. 500-513, April 2009, doi:10.1109/TMC.2008.151REFERENCES

- [1] A. Avin and B. Krishnamachari, “The Power of Choice in Random Walks: An Empirical Study,”
Proc. Ninth ACM/IEEE Int'l Symp. Modeling, Analysis, and Simulation of Wireless and Mobile Systems (MSWiM '06), 2006.- [2] C. Avin and G. Ercal, “On the Cover Time of Random Geometric Graphs,”
Proc. 32nd Int'l Colloquium Automata, Languages, and Programming (ICALP '05), 2005.- [3] C. Avin and C. Brito, “Efficient and Robust Query Processing in Dynamic Environment Using Random Walk Techniques,”
Proc. Third Int'l Symp. Information Processing in Sensor Networks (IPSN'04), 2004.- [4] Z. Bar-Yossef, R. Friedman, and G. Kliot, “RaWMS—Random Walk Based Lightweight Membership Service for Wireless AdHoc Networks,”
Proc. ACM MobiHoc, 2006.- [5] S. Boyd, A. Ghosh, B. Prabhakar, and D. Shah, “Gossip and Mixing Times of Random Walks on Random Graphs,”
Proc. SIAM Second Workshop Analytic Algorithmics and Combinatorics (ANALCO '05), 2005.- [6] R. Beraldi, L. Querzoni, and R. Baldoni, “A Hint-Based Probabilistic Protocol for Unicast Communications in MANETs,”
Elsevier J.Ad Hoc Networks, 2006.- [7] N. Chang and M. Liu, “Optimal Controlled Flooding Search in Large Wireless Networks,”
Proc. Third Int'l Symp. Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WIOPT '05), 2005.- [8] S. Dolev, E. Schiller, and J. Welch, “Random Walk for Self-Stabilizing Group Communication in Ad Hoc Networks,”
Proc. 21st ACM Symp. Principles of Distributed Computing (PODC '02), 2002.- [9] H. Dubois-Ferriere, M. Grossglauser, and M. Vetterli, “Age Matters: Efficient Route Discovery in Mobile Ad Hoc Networks Using Encounter Ages,”
Proc. ACM MobiHoc, 2004.- [10] C. Gkantsidis, M. Mihail, and A. Saberi, “Random Walks in Peer-to-Peer Networks: Algorithms and Evaluation,”
Elsevier Performance Evaluation J., vol. 63, no. 3, Mar. 2006.- [11] S. Ni, Y. Tseng, Y. Chen, and J. Sheu, “The Broadcast Storm Problem in a Mobile Ad Hoc Network,”
Proc. ACM MobiCom, Aug. 1999.- [12] D.B. Johnson and D.A. Maltz, “Dynamic Source Routing in Ad Hoc Wireless Networking,”
Mobile Computing, T. Iemielinski and H. Korth, eds., chapter 5, Kluwer Academic, 1996.- [13] J. Kopena et al., “Service-Based Computing on Manets: Enabling Dynamic Interoperability of First Responders,”
IEEE Intelligent Systems, Sept./Oct. 2005.- [14] G. Lau, M. Jaseemuddin, and G.M. Ravindran, “RAON: A P2P Network for MANET,”
Proc. Second IFIP Int'l Conf. Wireless and Optical Comm. Networks (WOCN '05), 2005.- [15] http://lrcwww.epfl.chRandomTrip/, 2008.
- [16] X. Li and J. Wu, “Searching Techniques in Peer-to-Peer Networks,”
Handbook of Theoretical and Algorithmic Aspects of Sensor, Auerbach Publications, 2006.- [17] L. Lovazs, “Random Walks on Graphs: A Survey,”
Combinatorics, Paul Erdos in Eighty, vol. 2, János Bolyai Math. Soc. Budapest, 1993.- [18] J. Luo and J.-P. Hubaux, “NASCENT: Network Layer Service for Vicinity Ad-Hoc Groups,”
Proc. First IEEE Conf. Sensor and Ad Hoc Comm. and Networks (SECON '04), 2004.- [19] Q. Lv, P. Cao, E. Cohen, K. Li, and S. Shenker, “Search and Replication in Unstructured Peer-to-Peer Networks,”
Proc. 16th Int'l Conf. Supercomputing (ICS '02), 2002.- [20] M. Gerla, C. Lindemann, and A. Rowstron, “Perspectives Workshop: Peer-to-Peer Mobile Ad Hoc Networks—New Research Issues,”
Proc. Dagstuhl Seminar, 2005.- [21] I. Goldhirsch and Y. Gefen, “Biased Random Walk on Networks,”
Physical Rev. A, vol. 35, no. 3, Feb. 1987.- [22] C. Gkantisidis, M. Michail, and A. Saberi, “Random Walks in Peer-to-Peer Networks,”
Proc. IEEE INFOCOM, 2004.- [23] M. Günes and O. Spaniol, “Ant-Routing-Algorithm for Mobile Multi-Hop Ad-Hoc Networks,”
Proc. Int'l Workshop Ad Hoc Networking (IWAHN '02), 2002.- [24] C.E. Perkins, E.M. Royer, and S.R. Das,
Ad-Hoc on Demand Distance Vector (AODV) Routing, IETF Internet draft, work in progress, July 2008.- [25] N. Sarafijanovic-Djukic and M. Grossglauser, “Last Encounter Routing under Random Waypoint Mobility,”
Proc. Third Int'l IFIP-TC6 Networking Conf. (NETWORKING '04), May 2004.- [26] S. Vempala,
Geometric Random Walks: A Survey, http://www-math. mit.edu/~vempala/papers survey.pdf, 2008. |