Oblivious Routing for Sensor Network Topologies

  • Costas BuschEmail author
  • Malik Magdon-Ismail
  • Jing Xi
Part of the Monographs in Theoretical Computer Science. An EATCS Series book series (EATCS)


We present oblivious routing algorithms whose routing paths are constructed independent of each other, with no dependence on the routing history. Oblivious algorithms are inherently adaptive to dynamic packet traffic, exhibit low congestion, and require low maintenance. All these attributes make oblivious algorithms to be suitable for sensor networks which are characterized by their limited energy and computational resources. Specifically, low congestion provides load balancing, and low stretch provides low-energy utilization. We present two simple oblivious routing algorithms. The first algorithm is for geometric networks in which nodes are embedded in the Euclidean plane. In this algorithm, a packet path is constructed by first choosing a random intermediate node in the space between the source and destination and then the packet is sent to its destination through the intermediate node. In the second algorithm we study mesh networks, where the nodes are arranged in a two-dimensional grid. Grids are interesting symmetric topologies which can be used as a testbed for designing efficient new routing algorithms in sensor networks. The oblivious algorithm in the mesh constructs the paths by decomposing the network into smaller submeshes in a hierarchical manner. This algorithm can be extended to d dimensions, which makes it suitable for three-dimensional sensor network deployments, such as in buildings and tall structures. We analyze the algorithms in terms of the stretch and congestion of the resulting paths and demonstrate that they exhibit near optimal performance.



We are grateful to the reviewers of this book chapter.


  1. 1.
    J. Aspens, Y. Azar, A. Fiat, S. Plotkin, and O. Waarts. Online load balancing with applications to machine scheduling and virtual circuit routing. In: Proceedings of the 25th ACM Symposium on Theory of Computing, pages 623–631, ACM Press, San Diego, California, USA, 1993.Google Scholar
  2. 2.
    F. Meyer auf der Heide, C. Schindelhauer, K. Volbert, and M. Grünewald. Congestion, dilation, and energy in radio networks. Theory of Computing Systems, 37(3):343–370, 2004.zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    B. Awerbuch and Y. Azar. Local optimization of global objectives: Competitive distributed deadlock resolution and resource allocation. In: Proceedings of 35th Annual Symposium on Foundations of Computer Science, pages 240–249, Santa Fe, NM, 1994.Google Scholar
  4. 4.
    Y. Azar, E. Cohen, A. Fiat, H. Kaplan, and H. Racke. Optimal oblivious routing in polynomial time. In: Proceedings of the 35th Annual ACM Symposium on Theory of Computing (STOC), San Diego, CA, ACM Press. pages 383–388, June 2003.Google Scholar
  5. 5.
    M. Bienkowski, M. Korzeniowski, and H. Räcke. A practical algorithm for constructing oblivious routing schemes. In: Proceedings of the 15th Annual ACM Symposium on Parallelism in Algorithms and Architectures, pages 24–33, ACM Press, San Diego, California, USA, June 2003.Google Scholar
  6. 6.
    A. Borodin and J. E. Hopcroft. Routing, merging, and sorting on parallel models of computation. Journal of Computer and System Science, 30:130–145, 1985.zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    C. Busch, M. Magdon-Ismail, and J. Xi. Oblivious routing on geometric networks. In: Proceedings of the 17th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), Las Vegas, NV, pages 316–324, July 2005.Google Scholar
  8. 8.
    C. Busch, M. Magdon-Ismail, and J. Xi. Optimal oblivious path selection on the mesh. IEEE Transactions on Computers, 57(5):660–671, May 2008.CrossRefMathSciNetGoogle Scholar
  9. 9.
    I. Chatzigiannakis, T. Dimitriou, S. Nikoletseas, and P. Spirakis. A probabilistic algorithm for efficient and robust data propagation in wireless sensor networks. Ad Hoc Networks, 4(5): 621 – 635, 2006.CrossRefGoogle Scholar
  10. 10.
    I. Chatzigiannakis, S. Nikoletseas, and P. G. Spirakis. Efficient and robust protocols for local detection and propagation in smart dust networks. Mobile Networks and Applications, 10(1–2):133–149, 2005.CrossRefGoogle Scholar
  11. 11.
    S. Dolev, T. Herman, and L. Lahiani. Polygonal broadcast, secret maturity, and the firing sensors. Ad Hoc Networks, 4(4):447 – 486, 2006.CrossRefGoogle Scholar
  12. 12.
    S. Dolev and N. Tzachar. Empire of colonies: Self-stabilizing and self-organizing distributed algorithm. Theoretical Computer Science, 410(6–7):514–532, 2009.zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    C. Efthymiou, S. Nikoletseas, and J. Rolim. Energy balanced data propagation in wireless sensor networks. Wireless Networks, 12(6):691–707, 2006.CrossRefGoogle Scholar
  14. 14.
    J. Gao and L. Zhang. Tradeoffs between stretch factor and load balancing ratio in routing on growth restricted graphs. In PODC ’04: Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing, New York, NY, pages 189–196, 2004.Google Scholar
  15. 15.
    C. Harrelson, K. Hildrum, and S. Rao. A polynomial-time tree decomposition to minimize congestion. In: Proceedings of the 15th Annual ACM Symposium on Parallelism in Algorithms and Architectures, pages 34–43, June 2003.Google Scholar
  16. 16.
    C. Intanagonwiwat, R. Govindan, D. Estrin, J. Heidemann, and F. Silva. Directed diffusion for wireless sensor networking. IEEE/ACM Transmission Network, 11(1):2–16, 2003.CrossRefGoogle Scholar
  17. 17.
    C. Kaklamanis, D. Krizanc, and T. Tsantilas. Tight bounds for oblivious routing in the hypercube. In: Proceedings of 2nd IEEE Symposium on Parallel and Distributed Processing (2nd SPAA 90), pages 31–36, Crete, Greece, July 1990.Google Scholar
  18. 18.
    F. T. Leighton, B. M. Maggs, and S. B. Rao. Packet routing and job-scheduling in \({O}(congestion+dilation)\) steps. Combinatorica, 14:167–186, 1994.zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    F. T. Leighton. Introduction to Parallel Algorithms and Architectures: Arrays - Trees - Hypercubes. Morgan Kaufmann, San Mateo, CA, 1992.zbMATHGoogle Scholar
  20. 20.
    T. Leighton, B. Maggs, and A. W. Richa. Fast algorithms for finding O(congestion + dilation) packet routing schedules. Combinatorica, 19:375–401, 1999.zbMATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    B. M. Maggs, F. Meyer auf der Heide, B. Vöcking, and M. Westerman. Exploiting locality in data management in systems of limited bandwidth. In: Proceedings of the 38th Annual Symposium on the Foundations of Computer Science, pages 284–293, IEEE, Miami Beach, Florida, USA, 1997.Google Scholar
  22. 22.
    F. Meyer auf der Heide and Berthold Vöcking. Shortest-path routing in arbitrary networks. Journal of Algorithms, 31(1):105–131, April 1999.zbMATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    R. Motwani and P. Raghavan. Randomized Algorithms. Cambridge University Press, Cambridge, 2000.Google Scholar
  24. 24.
    R. Ostrovsky and Y. Rabani. Universal O(congestion+dilation+\(\log^{1+\epsilon}{N})\) local control packet switching algorithms. In: Proceedings of the 29th Annual ACM Symposium on the Theory of Computing, New York, NY, pages 644–653, May 1997.Google Scholar
  25. 25.
    L. Popa, A. Rostamizadeh, R. Karp, C. Papadimitriou, and I. Stoica. Balancing traffic load in wireless networks with curveball routing. In: MobiHoc, 2007.Google Scholar
  26. 26.
    H. Räcke. Minimizing congestion in general networks. In: Proceedings of the 43rd Annual Symposium on the Foundations of Computer Science, pages 43–52, IEEE, Vancouver, Canada, November 2002.Google Scholar
  27. 27.
    H. Räcke. Data management and routing in general networks. Phd thesis, University of Paderborn, Paderborn, Germany, 2003.Google Scholar
  28. 28.
    H. Räcke. Optimal hierarchical decompositions for congestion minimization in networks. In: Proceedings of the 40th Annual ACM Symposium on Theory of Computing, pages 255–264, ACM Press, Victoria, British Columbia, Canada, May 2008.Google Scholar
  29. 29.
    P. Raghavan and C. D. Thompson. Randomized rounding: A technique for provably good algorithms and algorithmic proofs. Combinatorica, 7:365–374, 1987.zbMATHCrossRefMathSciNetGoogle Scholar
  30. 30.
  31. 31.
    A. Srinivasan and C-P. Teo. A constant factor approximation algorithm for packet routing, and balancing local vs. global criteria. In: Proceedings of the ACM Symposium on the Theory of Computing (STOC), pages 636–643, ACM Press, El Paso, Texas, USA, 1997.Google Scholar
  32. 32.
    L. G. Valiant. A scheme for fast parallel communication. SIAM Journal on Computing, 11:350–361, 1982.zbMATHCrossRefMathSciNetGoogle Scholar
  33. 33.
    L. G. Valiant and G. J. Brebner. Universal schemes for parallel communication. In: Proceedings of the 13th Annual ACM Symposium on Theory of Computing, pages 263–277, Milwaukee, Wisconsin, USA, May 1981.Google Scholar
  34. 34.
    F. Zhao and L. J. Guibas. Wireless Sensor Networks: An Information Processing Approach. Morgan Kaufmann, San Francisco, CA, USA, 2004.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Department of Computer ScienceLouisiana State UniversityBaton RougeUSA
  2. 2.Department of Computer ScienceRensselaer Polytechnic InstituteTroyUSA

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