Integer Maximum Flow in Wireless Sensor Networks with Energy Constraint

  • Hans L. Bodlaender
  • Richard B. Tan
  • Thomas C. van Dijk
  • Jan van Leeuwen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5124)


We study the integer maximum flow problem on wireless sensor networks with energy constraint. In this problem, sensor nodes gather data and then relay them to a base station, before they run out of battery power. Packets are considered as integral units and not splittable. The problem is to find the maximum data flow in the sensor network subject to the energy constraint of the sensors. We show that this integral version of the problem is strongly NP-complete and in fact APX-hard. It follows that the problem is unlikely to have a polynomial time approximation scheme. Even when restricted to graphs with concrete geometrically defined connectivity and transmission costs, the problem is still strongly NP-complete. We provide some interesting polynomial time algorithms that give good approximations for the general case nonetheless. For networks of bounded treewidth greater than two, we show that the problem is weakly NP-complete and provide pseudo-polynomial time algorithms. For a special case of graphs with treewidth two, we give a polynomial time algorithm.


Sensor Network Sensor Node Wireless Sensor Network Polynomial Time Source Node 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Hans L. Bodlaender
    • 1
  • Richard B. Tan
    • 1
    • 2
  • Thomas C. van Dijk
    • 1
  • Jan van Leeuwen
    • 1
  1. 1.Department of Information and Computing SciencesUtrecht UniversityUtrechtThe Netherlands
  2. 2.Department of Computer ScienceUniversity of Sciences & Arts of OklahomaChickashaUSA

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