Advertisement

The Maximum Energy-Constrained Dynamic Flow Problem

  • Sándor P. Fekete
  • Alexander Hall
  • Ekkehard Köhler
  • Alexander Kröller
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5124)

Abstract

We study a natural class of flow problems that occur in the context of wireless networks; the objective is to maximize the flow from a set of sources to one sink node within a given time limit, while satisfying a number of constraints. These restrictions include capacities and transit times for edges; in addition, every node has a bound on the amount of transmission it can perform, due to limited battery energy it carries. We show that this Maximum energy-constrained dynamic flow problem (ECDF) is difficult in various ways: it is NP-hard for arbitrary transit times; a solution using flow paths can have exponential-size growth; a solution using edge flow values may not exist; and finding an integral solution is NP-hard. On the positive side, we show that the problem can be solved polynomially for uniform transit times for a limited time limit; we give an FPTAS for finding a fractional flow; and, most notably, there is a distributed FPTAS that can be run directly on the network.

Keywords

Sensor Network Short Path Wireless Sensor Network Transit Time Battery Capacity 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aronson, J.E.: A survey of dynamic network flows. Annals of OR 20, 1–66 (1989)zbMATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    Bodlaender, H., Tan, R., van Dijk, T., van Leeuwen, J.: Integer maximum flow in wireless sensor networks with energy constraint. In: Proc. SWAT (2008)Google Scholar
  3. 3.
    Burkard, R.E., Dlaska, K., Klinz, B.: The quickest flow problem. ZOR — Methods and Models of Operations Research 37, 31–58 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Busse, M., Haenselmann, T., Effelsberg, W.: A comparison of lifetime-efficient forwarding strategies for wireless sensor networks. In: Proc. PE-WASUN, pp. 33–40 (2006)Google Scholar
  5. 5.
    Chang, J.-H., Tassiulas, L.: Maximum lifetime routing in wireless sensor networks. IEEE/ACM Transactions on Networking 12(4), 609–619 (2004)CrossRefGoogle Scholar
  6. 6.
    Fekete, S.P., Kröller, A.: Geometry-based reasoning for a large sensor network. In: Proc. SoCG, pp. 475–476 (2006)Google Scholar
  7. 7.
    Fekete, S.P., Kröller, A., Pfisterer, D., Fischer, S.: Algorithmic aspects of large sensor networks. In: Proc MSWSN, pp. 141–152 (2006)Google Scholar
  8. 8.
    Fekete, S.P., Schmidt, C., Wegener, A., Fischer, S.: Hovering data clouds for recognizing traffic jams. In: Proc. IEEE-ISOLA, pp. 213–218 (2006)Google Scholar
  9. 9.
    Fleischer, L., Skutella, M.: Quickest flows over time. SIAM Journal on Computing 36, 1600–1630 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Fleischer, L.K., Tardos, É.: Efficient continuous-time dynamic network flow algorithms. Operations Research Letters 23, 71–80 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Ford, L.R., Fulkerson, D.R.: Constructing maximal dynamic flows from static flows. Operations Research 6, 419–433 (1958)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Ford, L.R., Fulkerson, D.R.: Flows in Networks. Princeton University Press, Princeton (1962)zbMATHGoogle Scholar
  13. 13.
    Garg, N., Könemann, J.: Faster and simpler algorithms for multicommodity flow and other fractional packing problems. In: Proc. FOCS, p. 300 (1998)Google Scholar
  14. 14.
    Hall, A., Hippler, S., Skutella, M.: Multicommodity flows over time: Efficient algorithms and complexity. Theoretical Computer Science 379, 387–404 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Hoppe, B., Tardos, É.: The quickest transshipment problem. Mathematics of Operations Research 25, 36–62 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Hoppe, B.E.: Efficient dynamic network flow algorithms. PhD thesis, Cornell (1995)Google Scholar
  17. 17.
    Klinz, B., Woeginger, G.J.: Minimum cost dynamic flows: The series-parallel case. In: Balas, E., Clausen, J. (eds.) IPCO 1995. LNCS, vol. 920, pp. 329–343. Springer, Heidelberg (1995)Google Scholar
  18. 18.
    Kröller, A., Fekete, S.P., Pfisterer, D., Fischer, S.: Deterministic boundary recognition and topology extraction for large sensor networks. In: Proc. SODA, pp. 1000–1009 (2006)Google Scholar
  19. 19.
    Madan, R., Lall, S.: Distributed algorithms for maximum lifetime routing in wireless sensor networks. IEEE Transactions on Wireless Communications 5(8), 2185–2193 (2006)CrossRefGoogle Scholar
  20. 20.
    Madan, R., Luo, Z.-Q., Lall, S.: A distributed algorithm with linear convergence for maximum lifetime routing in wireless networks. In: Proc. Allerton Conference, pp. 896–905 (2005)Google Scholar
  21. 21.
    Peleg, D.: Distributed computing: a locality-sensitive approach. SIAM, Philadelphia (2000)zbMATHGoogle Scholar
  22. 22.
    Powell, W.B., Jaillet, P., Odoni, A.: Stochastic and dynamic networks and routing. In: Network Routing, ch. 3. Handbooks in Operations Research and Management Science, vol. 8, pp. 141–295. North–Holland, Amsterdam, The Netherlands (1995)Google Scholar
  23. 23.
    Ran, B., Boyce, D.E.: Modelling Dynamic Transportation Networks. Springer, Heidelberg (1996)Google Scholar
  24. 24.
    Sankar, A., Liu, Z.: Maximum lifetime routing in wireless ad-hoc networks. In: Proc. INFOCOM, pp. 1089–1097 (2004)Google Scholar
  25. 25.
    Schmid, S., Wattenhofer, R.: Algorithmic models for sensor networks. In: Proc. IPDPS (2006)Google Scholar
  26. 26.
    Wattenhofer, R.: Sensor networks: Distributed algorithms reloaded - or revolutions? In: Flocchini, P., Gąsieniec, L. (eds.) SIROCCO 2006. LNCS, vol. 4056, pp. 24–28. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  27. 27.
    Zussman, G., Segall, A.: Energy efficient routing in ad hoc disaster recovery networks. In: Proc. INFOCOM, pp. 682–691 (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Sándor P. Fekete
    • 1
  • Alexander Hall
    • 2
  • Ekkehard Köhler
    • 3
  • Alexander Kröller
    • 1
  1. 1.Algorithms GroupBraunschweig Institute of TechnologyBraunschweigGermany
  2. 2.EECS DepartmentUC BerkeleyUSA
  3. 3.Mathematical InstituteBrandenburg University of TechnologyCottbusGermany

Personalised recommendations