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Using Heterogeneity to Enhance Random Walk-based Queries

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Abstract

It is a well-known property of random walks that nodes with higher degree are visited more frequently. Based on this property, we propose the use of cluster-heads (high-degree nodes) together with a simple push-pull mechanism to enhance the performance of random walk-based querying: events are pushed towards high-degree nodes (cluster-heads) and pulled from the cluster-heads by a random-walk originated at the sink. Following this simple mechanism, we show that having even a small percentage of cluster-heads (degree-heterogeneity) can provide significant improvements in query performance. For linear topologies, we use connections between random walks and electrical resistances to prove that placing uniformly a fraction of 4/5k cluster-heads (where 2k is the degree of each cluster-head), can reduce querying costs from Θ(n 2) to Θ(n 2/k 2), an improvement of Θ(k 2). For more realistic two-dimensional topologies, we use Markov chain analysis and simulations to show a similar trend—using about 10% of the nodes as cluster-heads provides a query cost improvement between 30% and 70% depending on the coverage of the high-degree nodes.

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Notes

  1. Symmetry refers to a graph G′, where we name u as v and vice versa, is isomorphic to G.

  2. The proof of this result is not shown due to lack of space. However, it does not affect in anyway the result in Theorem 1. It is presented only on the interest of completeness.

  3. We are not certain about the reason for this value. Possibly, this is an scenario where the first local minima is not as good as a global minima.

References

  1. Krishnamachari, B., & Ahn, J. (2006). Optimizing data replication for expanding ring-based queries in wireless sensor networks. WiOpt.

  2. Ganesan, D., Krishnamachari, B., Woo, A., Culler, D., Estrin, D., & Wicker, S. (2002). Complex behavior at scale: an experimental study of low-power wireless sensor networks. UCLA CS Technical Report UCLA/CSD-TR 02-0013.

  3. Govindan, R., Kohler, E., Estrin, D., Bian, F., Chintalapudi, K., Gnawali, O., et al. (2005). Tenet: An architecture for tiered embedded networks. CENS Technical Report 56, November 10.

  4. Intanagonwiwat, C., Govindan, R., & Estrin, D. (2000). Directed diffusion: A scalable and robust communication paradigm for sensor networks. ACM Mobicom.

  5. Chang, N. B., & Liu, M. (2004). Revisiting the ttl-based controlled flooding search: Optimality and randomization. ACM MobiCom.

  6. Chang, N. B., & Liu, M. (2006). Controlled flooding search in a large network. IEEE/ACM Transactions on Networking, 15, 436–449.

    Article  Google Scholar 

  7. Cheng, Z., & Heinzelman, W. (2005). Flooding strategy for target discovery in wireless networks. ACM/Baltzer Wireless Networks.

  8. Cheng, Z., & Heinzelman, W. (2004). Searching strategy for multi-target discovery in wireless networks. ASWN.

  9. Aldous, D., & Fill, J. (1994). Reversible Markov chains and random walks on graphs. Draft monograph. http://www.stat.berkeley.edu/~aldous/RWG/book.html

  10. Lovasz, L. (1996). Random walks on graphs: A survey. In Combinatorics, Paul Erdos is eighty (Vol. 2, pp. 353–398). Janos Bolyai Mathematical Society, Budapest.

    Google Scholar 

  11. Burioni, R., & Cassi, D. (2005). Random walks on graphs: Ideas, techniques and results. Journal of Physics A: Mathematical and General, 38(8), Article R01, March.

  12. Fertr, M., Jeanvoine, E., Morin, C., & Rilling, L. (2005). Grid-aware operating system. Programming Parallel and Distributed Systems for Large Scale Numerical Simulation Applications.

  13. Cohen, E., & Shenker, S. (2002). Replication strategies in unstructured peer-to-peer networks. ACM SIGCOMM.

  14. Adamic, L. A., Lukose, R., Puniyani, A., & Huberman, B. (2001). Search in power-law networks. Physical Review E, 64, 46135.

    Article  Google Scholar 

  15. Chawathe, Y., Ratnasamy, S., Breslau, L., Lanham, N., & Shenker, S. (2003). Gia: Making gnutella like p2p systems scalable. ACM SIGCOMM.

  16. Tian, R., Xiong, Y., Zhang, Q., Li, B., Zhao, B. Y., & Li, X. (2005). Hybrid overlay structure based on random walks. IPTPS.

  17. Dolev, S., Schiller, E., & Welch, J. (2002). Random walk for self-stabilizing group communication in ad-hoc networks. SRDS.

  18. Bar-Yossef, Z., Friedman, R., Kliot, G. (2006). RaWMS—random walk based lightweight membership service for wireless Ad Hoc networks. MobiHoc.

  19. Sivaraj, H., & Gopalakrishnan, G. (2003). Random walk based heuristic algorithms for distributed memory model checking. PDMC.

  20. Henzinger, M. R., Heydon, A., Mitzenmacher, M., & Najork, M. (1999). Measuring index quality using random walks on the web. In 8th International world wide web conference, May.

  21. Servetto, S. D., & Barrenechea, G. (2002). Constrained random walks on random graphs: Routing algorithms for large scale wireless sensor networks. WSNA.

  22. Avin, C., & Brito, C. (2004). Efficient and robust query processing in dynamic environments using random walk techniques. Fontenay-aux-Roses: IPSN.

  23. Sadagopan, N., Krishnamachari, B., & Helmy, A. (2005). Active query forwarding in sensor networks (ACQUIRE). Journal of Ad Hoc Networks, Elsevier, 3(1), 91–113, January.

    Article  Google Scholar 

  24. Braginsky, D., & Estrin, D. (2002). Rumor routing algorithm for sensor networks. WSNA.

  25. Shakkottai, S. (2004). Asymptotics of query strategies over a sensor network. IEEE INFOCOM.

  26. Alanyali, M., Saligrama, V., & Savas, O. (2006). A random-walk model for distributed computation in energy-limited networks. In 1st workshop on information theory and its applications.

  27. Resnick, S. (1992). Adventures in stochastic processes (pp. 102–110). Birkhäuser, Boston.

    MATH  Google Scholar 

  28. Doyle, P., & Snell, J. (1984). Random walks and electric networks. MAA.

  29. Chandra, A., Raghavan, P., Ruzzo, W., Smolensky, R. (1989). The electrical resistance of a graph captures its commute and cover times. In ACM symposium on theory of computing.

  30. Zuniga, M., & Krishnamachari, B. (2007). An analysis of unreliability and asymmetry in low-power weireless links. ACM Transactions on Sensor Networks (TOSN), 3(2), June.

  31. Ahn, J., Kapadia, S., Pattem, S., Sridharan, A., Zuniga, M., Jun, J., et al. (2008). Analyzing the transitional region in low power wireless links. ACM CCR, in press.

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Authors and Affiliations

  1. Department of Electrical Engineering—Systems, University of Southern California, Los Angeles, CA, 90089-0781, USA

    Marco Zuniga & Bhaskar Krishnamachari

  2. Department of Communication Systems Engineering, Ben Gurion University of The Negev, Beer Sheva, 84105, Israel

    Chen Avin

Authors
  1. Marco Zuniga
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  2. Chen Avin
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  3. Bhaskar Krishnamachari
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Corresponding author

Correspondence to Marco Zuniga.

Additional information

This work was supported in part by NSF through grants numbered CNS-0325875, CNS-0347621, CNS-0435505, and CCF-0430061.

The work was done while the second author was a PostDoc at USC

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Zuniga, M., Avin, C. & Krishnamachari, B. Using Heterogeneity to Enhance Random Walk-based Queries . J Sign Process Syst Sign Image Video Technol 57, 401–414 (2009). https://doi.org/10.1007/s11265-008-0277-4

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  • DOI: https://doi.org/10.1007/s11265-008-0277-4

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