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Approximation Bounds for the Minimum \(k\)-Storage Problem

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Algorithms for Sensor Systems (ALGOSENSORS 2013)

Part of the book series: Lecture Notes in Computer Science ((LNCCN,volume 8243))

Abstract

Sensor networks are widely used to collect data that are required for future information retrieval. Data might be aggregated in a predefined number \(k\) of special nodes in the network, called storage nodes, which, for replying to external queries, compress the last received raw data and send them towards the sink. We consider the problem of locating such storage nodes in order to minimize the energy consumed for converging the raw data to the storage nodes as well as to converge the aggregated data to the sink. This is known as the minimum k-storage problem. We first prove that it is \(N\!P\)-hard to be approximated within a factor of \(1+\frac{1}{e}\). We then propose a local search algorithm which guarantees a constant approximation factor. We conducted extended experiments to show that the algorithm performs very well in many different scenarios. Further, we prove that the problem is not in APX if we consider directed links, unless \(P=N\!P\).

Research partially supported by the Research Grant 2010N5K7EB ‘PRIN 2010’ ARS TechnoMedia (Algoritmica per le Reti Sociali Tecno-mediate), from the Italian Ministry of University and Research, and by “Fondazione Cassa di Risparmio della Provincia dell’Aquila” within project ARISE.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Perugia, Italy

    Gianlorenzo D’Angelo, Daniele Diodati, Alfredo Navarra & Cristina M. Pinotti

Authors
  1. Gianlorenzo D’Angelo
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  2. Daniele Diodati
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  3. Alfredo Navarra
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  4. Cristina M. Pinotti
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Corresponding author

Correspondence to Gianlorenzo D’Angelo .

Editor information

Editors and Affiliations

  1. University of Ottawa, Ottawa, Ontario, Canada

    Paola Flocchini

  2. Stony Brook University, Stonybrook, New York, USA

    Jie Gao

  3. School of Computer Science, Carleton University, Ottawa, Ontario, Canada

    Evangelos Kranakis

  4. University of Paderborn, Paderborn, Germany

    Friedhelm Meyer auf der Heide

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D’Angelo, G., Diodati, D., Navarra, A., Pinotti, C.M. (2014). Approximation Bounds for the Minimum \(k\)-Storage Problem. In: Flocchini, P., Gao, J., Kranakis, E., Meyer auf der Heide, F. (eds) Algorithms for Sensor Systems. ALGOSENSORS 2013. Lecture Notes in Computer Science(), vol 8243. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45346-5_10

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  • DOI: https://doi.org/10.1007/978-3-642-45346-5_10

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-45345-8

  • Online ISBN: 978-3-642-45346-5

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