Partial is Full

  • Bernadette Charron-Bost
  • Matthias Függer
  • Jennifer L. Welch
  • Josef Widder
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6796)


Link reversal is the basis of several well-known routing algorithms [1,2,3]. In these algorithms, logical directions are imposed on the communication links and a node that becomes a sink reverses some of its incident links to allow the (re)construction of paths to the destination. In the Full Reversal (FR) algorithm [1], a sink reverses all its incident links. In other schemes, a sink reverses only some of its incident links; a notable example is the Partial Reversal (PR) algorithm [1]. Prior work [4] has introduced a generalization, called LR, of link-reversal routing, including FR and PR. In this paper, we show that every execution of LR on any link-labeled input graph corresponds, in a precise sense, to an execution of FR on a transformed graph. Thus, all the link reversal schemes captured by LR can be reduced to FR, indicating that “partial is full.” The correspondence preserves the work and time complexities. As a result, we can, for the first time, obtain the exact time complexity for LR, and by specialization for PR.


Time Complexity Directed Graph Sink Node Partial Reversal Route Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Gafni, E., Bertsekas, D.P.: Distributed algorithms for generating loop-free routes in networks with frequently changing topology. IEEE Transactions on Communications 29, 11–18 (1981)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Park, V.D., Corson, M.S.: A highly adaptive distributed routing algorithm for mobile wireless networks. In: 16th Conference on Computer Communications (Infocom), pp. 1405–1413 (1997)Google Scholar
  3. 3.
    Ko, Y.B., Vaidya, N.H.: Geotora: a protocol for geocasting in mobile ad hoc networks. In: Proceedings of the 2000 International Conference on Network Protocols, ICNP 2000, pp. 240–250 (2000)Google Scholar
  4. 4.
    Charron-Bost, B., Gaillard, A., Welch, J.L., Widder, J.: Routing without ordering. In: Proceedings of the 21st ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), pp. 145–153 (2009)Google Scholar
  5. 5.
    Malpani, N., Welch, J.L., Vaidya, N.: Leader election algorithms for mobile ad hoc networks. In: Proceedings of the 4th International Workshop on Discrete Algorithms and Methods for Mobile Computing and Communication (2000)Google Scholar
  6. 6.
    Derhab, A., Badache, N.: A self-stabilizing leader election algorithm in highly dynamic ad hoc mobile networks. IEEE Trans. Parallel Distrib. Syst. 19, 926–939 (2008)CrossRefzbMATHGoogle Scholar
  7. 7.
    Ingram, R., Shields, P., Walter, J.E., Welch, J.L.: An asynchronous leader election algorithm for dynamic networks. In: Proceedings of the IEEE International Parallel & Distributed Processing Symposium, pp. 1–12 (2009)Google Scholar
  8. 8.
    Chandy, K.M., Misra, J.: The drinking philosopher’s problem. ACM Transactions on Programming Languages and Systems 6, 632–646 (1984)CrossRefGoogle Scholar
  9. 9.
    Barbosa, V.C., Gafni, E.: Concurrency in heavily loaded neighborhood-constrained systems. ACM Trans. Program. Lang. Syst. 11, 562–584 (1989)CrossRefGoogle Scholar
  10. 10.
    Tirthapura, S., Herlihy, M.: Self-stabilizing distributed queuing. IEEE Transactions on Parallel and Distributed Systems 17, 646–655 (2006)CrossRefzbMATHGoogle Scholar
  11. 11.
    Raymond, K.: A tree-based algorithm for distributed mutual exclusion. ACM Transactions on Computer Systems 7, 61–77 (1989)CrossRefGoogle Scholar
  12. 12.
    Naimi, M., Trehel, M., Arnold, A.: A log(n) distributed mutual exclusion algorithm based on path reversal. J. Parallel and Distributed Computing 34, 1–13 (1996)CrossRefGoogle Scholar
  13. 13.
    Walter, J.E., Welch, J.L., Vaidya, N.H.: A mutual exclusion algorithm for ad hoc mobile networks. Wireless Networks 7, 585–600 (2001)CrossRefzbMATHGoogle Scholar
  14. 14.
    Charron-Bost, B., Függer, M., Welch, J.L., Widder, J.: Full reversal routing as a linear dynamical system. In: Kosowski, A., Yamashita, M. (eds.) SIROCCO 2011. LNCS, vol. 6796, pp. 99–110. Springer, Heidelberg (2011)Google Scholar
  15. 15.
    Busch, C., Surapaneni, S., Tirthapura, S.: Analysis of link reversal routing algorithms for mobile ad hoc networks. In: Proceedings of the 15th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), pp. 210–219 (2003)Google Scholar
  16. 16.
    Busch, C., Tirthapura, S.: Analysis of link reversal routing algorithms. SIAM Journal on Computing 35, 305–326 (2005)CrossRefzbMATHMathSciNetGoogle Scholar
  17. 17.
    Charron-Bost, B., Függer, M., Welch, J.L., Widder, J.: Partial is full. Research Report 10/2011, Technische Universität Wien, Institut für Technische Informatik, Treitlstr. 1-3/182-2, 1040 Vienna, Austria (2011)Google Scholar
  18. 18.
    Charron-Bost, B., Welch, J.L., Widder, J.: Link reversal: How to play better to work less. In: Dolev, S. (ed.) ALGOSENSORS 2009. LNCS, vol. 5804, pp. 88–101. Springer, Heidelberg (2009)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Bernadette Charron-Bost
    • 1
  • Matthias Függer
    • 2
  • Jennifer L. Welch
    • 3
  • Josef Widder
    • 3
  1. 1.CNRS, LIX, Ecole polytechniquePalaiseauFrance
  2. 2.TU WienAustria
  3. 3.Texas A&M UniversityUSA

Personalised recommendations