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Finding Degree Constrained k-Cardinality Minimum Spanning Trees for Wireless Sensor Networks

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Mobile Web and Intelligent Information Systems (MobiWIS 2018)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 10995))

Abstract

In this paper, we consider the degree constrained k-cardinality minimum spanning tree network problem (k-DCMST). This problem arises as a combination of two classical optimization problems, namely the degree constrained and k-minimum spanning tree problems (Resp. DCMST and k-MST). Let G(V, E) be a connected undirected graph formed with vertex and edge sets V and E, respectively. The DCMST problem asks for a minimum spanning tree where each maximum vertex degree is limited to a certain constant d lower than the cardinality of V minus one whilst the k-MST asks for a minimum spanning sub-tree formed with k nodes chosen from set V. Consequently, the k-DCMST asks for a sub-tree formed with k vertices where each vertex has degree lower than or equal to d. This problem is mainly motivated from the domain of wireless sensor networks where connected backbone sub-tree topologies will be mandatorily required for future technologies in order to connect any network under the internet of things paradigm. Vertex degree constraints arise naturally in order to avoid overloaded nodes in the network. We propose two compact formulations for this problem. More precisely, a Miller-Tucker-Zemlin constrained version and a single flow based formulation that we further strengthen by using the Handshaking lemma and with valid inequalities adapted from the DCMST and dominating tree problems. Numerical results are given for complete and disk graph instances for different degree values. Our preliminary numerical results indicate that the flow based model allows one to obtain optimal solutions in less CPU time for most of the instances.

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Acknowledgments

The authors acknowledge the financial support of Dicyt project 061713AS of VRIDi/USACH, Fondef IT17M10012, and Beca Doctorado Nacional 2016 CONICYT (PFCHA) 21161397.

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Authors and Affiliations

  1. Departamento de Ingeniería Eléctrica, Universidad de Santiago de Chile, Avenida Ecuador 3519, Santiago, Chile

    Pablo Adasme, Ismael Soto & Fabian Seguel

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  1. Pablo Adasme
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  2. Ismael Soto
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  3. Fabian Seguel
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Corresponding author

Correspondence to Pablo Adasme .

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Editors and Affiliations

  1. Oxford Brookes University, Oxford, United Kingdom

    Muhammad Younas

  2. University of Bradford, Bradford, United Kingdom

    Irfan Awan

  3. Brunel University London, Uxbridge, United Kingdom

    George Ghinea

  4. i2CAT, Barcelona, Spain

    Marisa Catalan Cid

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Adasme, P., Soto, I., Seguel, F. (2018). Finding Degree Constrained k-Cardinality Minimum Spanning Trees for Wireless Sensor Networks. In: Younas, M., Awan, I., Ghinea, G., Catalan Cid, M. (eds) Mobile Web and Intelligent Information Systems. MobiWIS 2018. Lecture Notes in Computer Science(), vol 10995. Springer, Cham. https://doi.org/10.1007/978-3-319-97163-6_5

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  • DOI: https://doi.org/10.1007/978-3-319-97163-6_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-97162-9

  • Online ISBN: 978-3-319-97163-6

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