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Assigning Sensors to Missions with Demands

  • Conference paper
Algorithmic Aspects of Wireless Sensor Networks (ALGOSENSORS 2007)

Abstract

We introduce Semi-Matching with Demands (SMD), which models a certain problem in sensor networks of assigning individual sensors to sensing tasks. If there are multiple sensing tasks or missions to be accomplished simultaneously, and if sensor assignment must be exclusive, then this is a bipartite semi-matching problem. Each mission is associated with a demand value and a profit value; each sensor-mission pair is associated with a utility offer (possibly 0). The goal is a sensor assignment that maximizes the profits of the satisfied missions (with no credit for partially satisfied missions). SMD is NP-hard and as hard to approximate as Maximum Independent Set. Therefore we investigate less difficult constrained versions of the problem. We give a simple greedy Δ-approximation algorithm for a degree-constrained version (Δ-SMD), in which each mission receives positive utility offers from at most Δ sensors. For small Δ, we show that Δ-SMD is equivalent to k-Set Packing (with k = Δ), which yields a polynomial-time (Δ+1)/2-approximation. For Δ= 2, we solve the problem optimally by reduction to maximum matching. Finally, we introduce a geometric version which remains strongly NP-hard but has a PTAS.

Research was sponsored by the U.S. Army Research Laboratory and the U.K. Ministry of Defence and was accomplished under Agreement Number W911NF-06-3-0001. The views and conclusions contained in this document are those of the author(s) and should not be interpreted as representing the official policies, either expressed or implied, of the U.S. Army Research Laboratory, the U.S. Government, the U.K. Ministry of Defence or the U.K. Government. The U.S. and U.K. Governments are authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation hereon. We thank Panos Hilaris for delivering the workshop presentation.

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Mirosław Kutyłowski Jacek Cichoń Przemysław Kubiak

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Bar-Noy, A., Brown, T., Johnson, M.P., La Porta, T., Liu, O., Rowaihy, H. (2008). Assigning Sensors to Missions with Demands. In: Kutyłowski, M., Cichoń, J., Kubiak, P. (eds) Algorithmic Aspects of Wireless Sensor Networks. ALGOSENSORS 2007. Lecture Notes in Computer Science, vol 4837. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77871-4_11

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  • DOI: https://doi.org/10.1007/978-3-540-77871-4_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-77870-7

  • Online ISBN: 978-3-540-77871-4

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