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The Maximum Distance-d Independent Set Problem on Unit Disk Graphs

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Frontiers in Algorithmics (FAW 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10823))

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Abstract

In this article, we study the maximum distance-d independent set problem, a variant of the maximum independent set problem, on unit disk graphs. We first show that the problem is NP-hard. Next, we propose a polynomial-time constant-factor approximation algorithm and a PTAS for the problem.

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Notes

  1. 1.

    The length of a smallest cycle.

  2. 2.

    By independent we mean for any \(p_i \in H_i \cap P\) and \(p_j \in H_j \cap P\), \(p_i\) and \(p_j\) are distance-d independent and also, \(OPT^i \cap OPT^j = \emptyset \).

  3. 3.

    If there are two components of \(G_\chi \) having distance less than d in G, then we can view them as a single component.

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Acknowledgements

The authors would like to thank the anonymous referees for their valuable comments and suggestions.

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Authors and Affiliations

  1. Indian Institute of Technology, Guwahati, India

    Sangram K. Jena & Gautam K. Das

  2. Indian Statistical Institute, Kolkata, India

    Ramesh K. Jallu & Subhas C. Nandy

Authors
  1. Sangram K. Jena
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  2. Ramesh K. Jallu
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  3. Gautam K. Das
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  4. Subhas C. Nandy
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Corresponding author

Correspondence to Gautam K. Das .

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Editors and Affiliations

  1. Texas A&M University, College Station, Texas, USA

    Jianer Chen

  2. Shanghai University of Finance and Economics, Shanghai, China

    Pinyan Lu

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Jena, S.K., Jallu, R.K., Das, G.K., Nandy, S.C. (2018). The Maximum Distance-d Independent Set Problem on Unit Disk Graphs. In: Chen, J., Lu, P. (eds) Frontiers in Algorithmics. FAW 2018. Lecture Notes in Computer Science(), vol 10823. Springer, Cham. https://doi.org/10.1007/978-3-319-78455-7_6

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  • DOI: https://doi.org/10.1007/978-3-319-78455-7_6

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