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Classification of Solutions to the Minimum Energy Problem in One Dimensional Sensor Networks

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Computer Networks (CN 2016)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 608))

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Abstract

We classify of the minimum energy problem in one dimensional wireless sensor networks for the data transmission cost matrix which is a power function of the distance between transmitter and receiver with any real exponent. We show, how these solutions can be utilized to solve the minimum energy problem for the data transmission cost matrix which is a linear combination of two power functions. We define the minimum energy problem in terms of the sensors signal power, transmission time and capacities of transmission channels. We prove, that for the point-to-point data transmission method utilized by the sensors in the physical layer, when the transmitter adjust the power of its radio signal to the distance to the receiver, the optimal transmission is without interference. We also show, that the solutions of the minimum energy problem written in terms of data transmission cost matrix and in terms of the sensor signal power coincide.

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Authors and Affiliations

  1. Institute of Mathematics and Informatics, Opole University, Opole, Poland

    Zbigniew Lipiński

Authors
  1. Zbigniew Lipiński
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Correspondence to Zbigniew Lipiński .

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Editors and Affiliations

  1. Silesian University of Technology, Gliwice, Poland

    Piotr Gaj

  2. Silesian University of Technology, Gliwice, Poland

    Andrzej Kwiecień

  3. Silesian University of Technology, Gliwice, Poland

    Piotr Stera

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Lipiński, Z. (2016). Classification of Solutions to the Minimum Energy Problem in One Dimensional Sensor Networks. In: Gaj, P., Kwiecień, A., Stera, P. (eds) Computer Networks. CN 2016. Communications in Computer and Information Science, vol 608. Springer, Cham. https://doi.org/10.1007/978-3-319-39207-3_6

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  • DOI: https://doi.org/10.1007/978-3-319-39207-3_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-39206-6

  • Online ISBN: 978-3-319-39207-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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