Approximation Algorithms for Power-Aware Scheduling of Wireless Sensor Networks with Rate and Duty-Cycle Constraints

  • Rajgopal Kannan
  • Shuangqing Wei
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4026)


We develop algorithms for finding the minimum energy transmission schedule for duty-cycle and rate constrained wireless sensor nodes transmitting over an interference channel. Since traditional optimization methods using Lagrange multipliers do not work well and are computationally expensive given the non-convex constraints, we develop fully polynomial approximation schemes (FPAS) for finding optimal schedules by considering restricted versions of the problem using multiple discrete power levels. We first show a simple dynamic programming solution that optimally solves the restricted problem. For two fixed transmit power levels (0 and P), we then develop a 2-factor approximation for finding the optimal fixed transmission power level per time slot, P opt , that generates the optimal (minimum) energy schedule. This can then be used to develop a (2, 1+ε)-FPAS that approximates the optimal power consumption and rate constraints to within factors of 2 and arbitrarily small ε> 0, respectively. Finally, we develop an algorithm for computing the optimal number of discrete power levels per time slot (O(1/ε)), and use this to design a (1, 1+ε)-FPAS that consumes less energy than the optimal while violating each rate constraint by at most a 1+ε factor.


Wireless Sensor Network Time Slot Power Level Feasible Schedule Rate Constraint 
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.


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  1. 1.
    Singh, S., Raghavendra, C.: Pamas: Power aware multi-access protocol with signalling for ad hoc networks (1999)Google Scholar
  2. 2.
    Ye, W., Heidemann, J., Estrin, D.: An energy-efficient mac protocol for wireless sensor networks (2002)Google Scholar
  3. 3.
    Ye, W., Heidemann, J., Estrin, D.: Medium access control with coordinated, adaptive sleeping for wireless sensor networks (2003)Google Scholar
  4. 4.
    Uysal-Biyikoglu, E., Prabhakar, B., El Gamal, A.: Energy-efficient packet transmission over a wireless link. IEEE/ACM Transactions on Networking 10, 487–499 (2002)CrossRefGoogle Scholar
  5. 5.
    Uysal-Biyikoglu, E., Gamal, A.E.: On adaptive transmission for energy efficiency in wireless data networks. IEEE Trans. Inform. Theory (2004)Google Scholar
  6. 6.
    Hanly, S., Tse, D.: Power control and capacity of spread-spectrum wireless networks. Automat. 35(12), 1987–2012 (1999)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Wang, K., Chiasserini, C., Rao, R., Proakis, J.: A distributed joint scheduling and power control algorithm for multicasting in wireless ad hoc networks. In: IEEE International Conference on Communications, 2003. ICC 2003, vol. 1, pp. 725–731 (2003)Google Scholar
  8. 8.
    ElBatt, T., Ephremides, A.: Joint scheduling and power control for wireless ad hoc networks. IEEE Transactions on Wireless Communications 3, 74–85 (2004)CrossRefGoogle Scholar
  9. 9.
    Foschini, G.J., Miljanic, Z.: A simple distributed autonomous power control algorithm and its convergence. IEEE Transactions on Vehicular Technology, 641–646 (1993)Google Scholar
  10. 10.
    Bambos, N.: Toward power-sensitive network architectures in wireless communications: concepts, issues, and design concepts. IEEE Personal Communications, 50–59 (1998)Google Scholar
  11. 11.
    Bambos, N., Kandukuri, S.: Power control multiple access (pcma). Wireless Networks (1999)Google Scholar
  12. 12.
    Bertsekas, D.P.: Nonlinear Programming. In: Athena Scientific, 2nd edn., Belmont, Massachusetts (1999)Google Scholar
  13. 13.
    Bertsekas, D., Lauer, G., Sandell, N., Posbergh, T.: Optimal short-term scheduling of large-scale power systems. IEEE Transactions on Automatic Control, 1–11 (1983)Google Scholar
  14. 14.
    Dorit Hochbaum, E.: Approximation Algorithms for NP-Hard Problems, 1st edn. PWS Publishing Company, Boston, MA (1997)Google Scholar
  15. 15.
    Martello, S., Toth, P.: Knapsack Problems, 1st edn. J. Wiley and Sons, Chichester (1990)MATHGoogle Scholar
  16. 16.
    Kannan, R., Wei, S., Chakravarthi, V., Seetharaman, G.: Using misbehavior to analyze strategic versus aggregate energy minimization in wireless sensor networks (2006)Google Scholar
  17. 17.
    Kannan, R., Wei, S.: Lsu-cs-tr-06-3. Technical report, LSU (2006)Google Scholar
  18. 18.
    Cover, T.M., Thomas, J.A.: Elements of Information Theory, 1st edn. Wiley, New York (1991)MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Rajgopal Kannan
    • 1
  • Shuangqing Wei
    • 2
  1. 1.Department of Computer Science 
  2. 2.Department of Electrical and Computer EngineeringLouisiana State UniversityBaton RougeUSA

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