Abstract
Coverage and security of network nodes are the critical issue in wireless sensor networks. The covering number is an essential tool in monitoring networks, as it gives the smallest number of detection devices needed to identify the location of an intruder or a malicious node. In this paper, we provide a graph theory based approach which could be beneficial to keep the network secure. The covering number for circulant networks are calculated exactly and their theoretical properties are explored in this article. Circulant networks have a broad range of applications in parallel computing and signal processing because of its increased connectivity. The minimal vertex covering set of a network serves as its back bone in the process of routing.
Similar content being viewed by others
References
Angel, D., & Amutha, A. (2012). Optimal covering on hypercube networks. Lecture Notes in Information Technology, 38, 522–528.
Angel, D., & Amutha, A. (2015). Exact covering on butterfly and Benes networks. International Journal of Pure and Applied Mathematics, 101(6), 863–872.
Balaji, S., Swaminathan, V., & Kannan, K. A. (2010). Simple algorithm to optimize maximum independent set. Advanced Modeling and Optimization, 12(1), 107–118.
Bermond, J. C., Comellas, F., & Hsu, D. F. (1995). Distributed loop computer networks. A survey. Journal of Parallel and Distributed Computing, 24(1), 2–10.
Bhat, P. G., & Bhat, R. S. (2012). Inverse independence number of a graph. International Journal of Computer Applications, 42(5), 9–13.
Boesch, F. T., & Wang, J. (1985). Reliable circulant networks with minimum transmission delay. IEEE Transactions on Circuit and Systems, 32(12), 1286–1291.
Chena, J., Linb, Y., Li, J., Lina, G., Maa, Z., & Tan, A. (2016). A rough set method for the minimum vertex cover problem of graphs. Applied Soft Computing, 42, 360–367.
Hochbaum, D. (1983). Efficient bounds for the stable set, vertex cover and set packing problem. Discrete Applied Mathematics, 6(3), 243–254.
Jianhua, T. (2015). A fixed-parameter algorithm for the vertex cover P3 problem. Information Processing Letters, 115(2), 96–99.
Karakostas, G. (2005). A better approximation ratio for the vertex cover problem. Lecture Notes in Computer Science, 3580, 1043–1050.
Micu, D., & De Mey, G. (2013). The condition number for circulant networks. Électrotechnique et Electroenergetique, 58(2), 115–122.
Norman, R. Z., & Rabin, M. O. (1959). An algorithm for a minimum cover of a graph. Proceedings of the American Mathematical Society, 10, 315–319.
Pattillo, J., & Butenko, S. (2013). On the maximum quasi-clique problem. Discrete Applied Mathematics, 161(1), 244–257.
Sáenz-de-Cabezón, E., & Wynn, H. P. (2014). Measuring the robustness of a network using minimal vertex covers. Mathematics and Computers in Simulation, 104, 82–94.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Angel, D., Amutha, A. On Covering the Nodes of Circulant Networks and Its Applications. Wireless Pers Commun 94, 2163–2172 (2017). https://doi.org/10.1007/s11277-016-3367-9
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11277-016-3367-9