Construction of Minimum Power 3-Connected Subgraph with k Backbone Nodes in Wireless Sensor Networks

  • D. Pushparaj Shetty
  • M. Prasanna LakshmiEmail author
Conference paper
Part of the Trends in Mathematics book series (TM)


Minimizing the total power in a wireless sensor network (WSN) has great significance, since the nodes are powered by a small battery of limited capacity. By using an appropriate topology, the energy utilization of the network can be minimized which results in an increased lifetime of a WSN. In reality, WSN is modeled as an undirected graph in which each vertex represents a sensor node and an edge represents the link between the two sensor nodes. We define a distance function that maps a pair of vertices to a positive real number, i.e., Euclidean distance between the two vertices. On this initial topology, we construct a reduced topology satisfying special connectivity constraints like bi-connectivity, k-connectivity, bounded diameter, degree restricted, etc. We assign power to each node as the maximum distance of all its adjacent edges, and total power of the network is the sum of the powers of all the vertices. Fault tolerance addresses the issue of a node or link failure in a WSN. Fault-tolerant network aims at k-connectivity in the network so that there exist at least k vertex disjoint paths between any two sensor nodes of the network. Minimum power 2-connected subgraph (MP2CS) problem is to contrive a 2-connected network with minimum total power. It is proved that MP2CS problem is NP-hard. Minimum power k backbone node 2-connected subgraph (MPkB2CS) problem is a special case of MP2CS problem, which seeks a power assignment satisfying 2-connectivity with k backbone nodes. In this paper, the problem of finding a 3-connected network for a given set of nodes, which minimizes the total power with k backbone nodes, is addressed which is termed as MPkB3CS problem. We propose an algorithm for MPkB3CS problem and establish that the proposed algorithm has an approximation ratio of 4k + 1, for k ≥ 3.


Wireless sensor networks Graph algorithms Topology control problem Range assignment Approximation algorithm 



The authors would like to acknowledge the National Institute of Technology Karnataka, Surathkal, for the support in this research work.


  1. 1.
    Akyildiz, I.F., Su, W., Sankarasubramaniam, Y., Cayirci, E.: Wireless sensor networks: a survey. Computer Networks 38(4), 393–422 (2002), CrossRefGoogle Scholar
  2. 2.
    Azharuddin, M., Kuila, P., Jana, P.K.: Energy efficient fault tolerant clustering and routing algorithms for wireless sensor networks. Computers & Electrical Engineering 41, 177–190 (2015), CrossRefGoogle Scholar
  3. 3.
    Călinescu, G., Wan, P.: Range assignment for high connectivity in wireless ad hoc networks. In: Ad-Hoc, Mobile, and Wireless Networks, Second International Conference, ADHOC-NOW 2003 Montreal, Canada, October 8-10, 2003, Proceedings. pp. 235–246 (2003),
  4. 4.
    Cheng, X., Narahari, B., Simha, R., Cheng, M.X., Liu, D.: Strong minimum energy topology in wireless sensor networks: Np-completeness and heuristics. IEEE Trans. Mob. Comput. 2(3), 248–256 (2003), CrossRefGoogle Scholar
  5. 5.
    Fuchs, B.: On the hardness of range assignment problems. Networks 52(4), 183–195 (2008), MathSciNetCrossRefGoogle Scholar
  6. 6.
    Lando, Y., Nutov, Z.: On minimum power connectivity problems. J. Discrete Algorithms 8(2), 164–173 (2010), MathSciNetCrossRefGoogle Scholar
  7. 7.
    Li, X., Zhang, Z.: Two algorithms for minimum 2-connected r-hop dominating set. Inf. Process. Lett. 110(22), 986–991 (2010), MathSciNetCrossRefGoogle Scholar
  8. 8.
    Lloyd, E.L., Liu, R., Marathe, M.V., Ramanathan, R., Ravi, S.S.: Algorithmic aspects of topology control problems for ad hoc networks. MONET 10(1-2), 19–34 (2005), Google Scholar
  9. 9.
    Nutov, Z.: Approximating minimum-power k-connectivity. In: Ad-hoc, Mobile and Wireless Networks, 7th International Conference, ADHOC-NOW 2008, Sophia-Antipolis, France, September 10-12, 2008, Proceedings. pp. 86–93 (2008),
  10. 10.
    Panda, B.S., Shetty, D.P.: Strong minimum energy hierarchical topology in wireless sensor networks. J. Comb. Optim. 32(1), 174–187 (2016), MathSciNetCrossRefGoogle Scholar
  11. 11.
    Panda, B.S., Shetty, D.P.: Minimum range assignment problem for two connectivity in wireless sensor networks. In: Distributed Computing and Internet Technology - 10th International Conference, ICDCIT 2014, Bhubaneswar, India, February 6-9, 2014. Proceedings. pp. 122–133 (2014),
  12. 12.
    Ramanathan, R., Hain, R.: Topology control of multihop wireless networks using transmit power adjustment. In: Proceedings IEEE INFOCOM 2000, The Conference on Computer Communications, Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies, Reaching the Promised Land of Communications, Tel Aviv, Israel, March 26-30, 2000. pp. 404–413 (2000),
  13. 13.
    Santi, P.: Topology control in wireless ad hoc and sensor networks. Wiley (2005)Google Scholar
  14. 14.
    Vempala, S., Vetta, A.: Factor 4/3 Approximations for Minimum 2-Connected Subgraphs, pp. 262–273. Springer Berlin Heidelberg, Berlin, Heidelberg (2000),
  15. 15.
    West, D.B., et al.: Introduction to graph theory, vol. 2. Prentice hall Upper Saddle River (2001)Google Scholar
  16. 16.
    Zheng, C., Yin, L., Zhang, Y.: Constructing r-hop 2-connected dominating sets for fault-tolerant backbone in wireless sensor networks. In: 2012 8th International Conference on Wireless Communications, Networking and Mobile Computing. pp. 1–4 (Sept 2012)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.National Institute of Technology KarnatakaMangaluruIndia

Personalised recommendations