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Distributed Dominating Sets in Interval Graphs

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Computing and Combinatorics (COCOON 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13595))

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Abstract

The Minimum Dominating Set (MMDS) and Minimum Connected Dominating set (MMCDS) problems are well-studied in the distributed communities due to their numerous applications across the field. These problems are also crucial in wireless ad hoc networks, mainly for the particular type of geometric graphs. We study these problems in geometric graphs such as interval and unit interval graphs. We exploit the underlying geometric structures of these graph classes and present either constant factors distributed algorithms in constant rounds or algorithms with matching lower bounds in the \(\mathcal {LOCAL}\) communication model.

The authors acknowledge the support of the Science and Engineering Research Board (SERB), Department of Science and Technology, Govt. of India (grant no. CRG/2020/005964). Dr. Barun Gorain also acknowledges the support of the Science and Engineering Research Board (SERB), Department of Science and Technology, Govt. of India (grant no. MTR/2021/000118), and the Research Initiation Grant supported by the Indian Institute of Technology Bhilai, India.

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Notes

  1. 1.

    Here and throughout ties are broken by considering the maximum length node.

References

  1. Amiri, S.A., de Mendez, P.O., Rabinovich, R., Siebertz, S.: Distributed domination on graph classes of bounded expansion. In: SPAA, pp. 143–151 (2018)

    Google Scholar 

  2. Cheng, X., Ding, M., Du, D.H., Jia, X.: Virtual backbone construction in multihop ad hoc wireless networks. Wirel. Commun. Mob. Comput. 6, 183–190 (2006)

    Article  Google Scholar 

  3. Das, B., Bharghavan, V.: Routing in ad-hoc networks using minimum connected dominating sets. In: ICC, pp. 376–380 (1997)

    Google Scholar 

  4. Das, B., Sivakumar, R., Bharghavan, V.: Routing in ad hoc networks using a spine. In: ICCCN, pp. 34–41 (1997)

    Google Scholar 

  5. Funke, S., Kesselman, A., Meyer, U., Segal, M.: A simple improved distributed algorithm for minimum CDS in unit disk graphs. ACM Trans. Sens. Netw. 2(3), 444–453 (2006)

    Article  Google Scholar 

  6. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, New York (1979)

    MATH  Google Scholar 

  7. Ghaffari, M., Kuhn, F., Maus, Y.: On the complexity of local distributed graph problems. In: STOC 2017, pp. 784–797 (2017)

    Google Scholar 

  8. Gorain, B., Mondal, K., Pandit, S.: Distributed independent sets in interval and segment intersection graphs. In: SOFSEM, pp. 175–188 (2021)

    Google Scholar 

  9. Jallu, R.K., Prasad, P.R., Das, G.K.: Distributed construction of connected dominating set in unit disk graphs. J. Parallel Distrib. Comput. 104, 159–166 (2017)

    Article  Google Scholar 

  10. Karp, R.M.: Reducibility among combinatorial problems. In: Miller, R.E., Thatcher, J.W., Bohlinger, J.D. (eds.) Complexity of Computer Computations. IRSS, pp. 85–103. Springer, Boston (1972). https://doi.org/10.1007/978-1-4684-2001-2_9

  11. Kuhn, F., Moscibroda, T., Wattenhofer, R.: Local computation: lower and upper bounds. J. ACM 63, 17:1–17:44 (2016)

    Google Scholar 

  12. Min, M., Du, H., Jia, X., Huang, C.X., Huang, S.C., Wu, W.: Improving construction for connected dominating set with Steiner tree in wireless sensor networks. J. Global Optimiz. 35(1), 111–119 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  13. Molla, A.R., Pandit, S., Roy, S.: Optimal deterministic distributed algorithms for maximal independent set in geometric graphs. J. Parallel Distrib. Comput. 132, 36–47 (2019)

    Article  Google Scholar 

  14. Peleg, D.: Distributed Computing: A Locality-Sensitive Approach. Society for Industrial and Applied Mathematics (2000)

    Google Scholar 

  15. Stojmenovic, I., Seddigh, M., Zunic, J.D.: Dominating sets and neighbor elimination-based broadcasting algorithms in wireless networks. IEEE Trans. Parallel Distrib. Syst. 13, 14–25 (2002)

    Article  Google Scholar 

  16. Wan, P., Alzoubi, K.M., Frieder, O.: Distributed construction of connected dominating set in wireless ad hoc networks. In: INFOCOM, pp. 1597–1604 (2002)

    Google Scholar 

  17. Wu, J., Li, H.: On calculating connected dominating set for efficient routing in ad hoc wireless networks. In: DIAL-M, pp. 7–14 (1999)

    Google Scholar 

  18. Wu, W., Du, H., Jia, X., Li, Y., Huang, S.C.: Minimum connected dominating sets and maximal independent sets in unit disk graphs. Theor. Comput. Sci. 352(1–3), 1–7 (2006)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Indian Institute of Technology Bhilai, Raipur, Chattisgarh, India

    Barun Gorain

  2. Indian Institute of Technology Ropar, Rupnagar, Punjab, India

    Kaushik Mondal

  3. Dhirubhai Ambani Institute of Information and Communication Technology, Gandhinagar, Gujarat, India

    Supantha Pandit

Authors
  1. Barun Gorain
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  2. Kaushik Mondal
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  3. Supantha Pandit
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Corresponding author

Correspondence to Supantha Pandit .

Editor information

Editors and Affiliations

  1. Shenzhen Institute of Advanced Technology, Shenzhen, China

    Yong Zhang

  2. Harbin Institute of Technology, Harbin, China

    Dongjing Miao

  3. Technical University of Berlin, Berlin, Germany

    Rolf Möhring

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Gorain, B., Mondal, K., Pandit, S. (2022). Distributed Dominating Sets in Interval Graphs. In: Zhang, Y., Miao, D., Möhring, R. (eds) Computing and Combinatorics. COCOON 2022. Lecture Notes in Computer Science, vol 13595. Springer, Cham. https://doi.org/10.1007/978-3-031-22105-7_45

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  • DOI: https://doi.org/10.1007/978-3-031-22105-7_45

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-22104-0

  • Online ISBN: 978-3-031-22105-7

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