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Comparison between Maximal Independent Sets and Maximal Cliques Models to Calculate the Capacity of Multihop Wireless Networks

  • Maher HealEmail author
  • Jingpeng Li
Conference paper
Part of the Lecture Notes in Networks and Systems book series (LNNS, volume 70)

Abstract

In this work we compare two models to calculate the capacity of multihop wireless networks. The first model utilizes the maximal independent sets of the conflict graph. The problem in that model is formulated as a linear program. The second model in our comparison utilizes the maximal cliques of the conflict graph using integer programming. We see the second model is much more efficient in calculating the capacity for larger networks. We make no assumption on the interference models and we only model it by assuming a conflict matrix. First, we prove there is a periodic schedule for the flow, by using that we formulate our integer programming model to attain maximum capacity for the network. We consider one source of data and one destination i.e. a single commodity network.

Keywords

Maximal independent set Maximal clique Linear programming Binary programming Maximum throughput 

References

  1. 1.
    Franceschetti, M., Dousse, O., David, N., Thiran, P.: Closing the gap in the capacity of wireless networks via percolation theory. IEEE Trans. Inf. Theory 53(3), 1009–1018 (2007)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Gupta, P., Kumar, P.R.: The capacity of wireless networks. IEEE Trans. Inf. theory 46(2), 388–404 (2000)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Hou, Y., Li, M., Zeng, K.: Throughput optimization in multi-hop wireless networks with reconfigurable antennas. In: 2017 International Conference on Computing, Networking and Communications (ICNC), pp. 620–626. IEEE (2017)Google Scholar
  4. 4.
    Hu, C., Wang, X., Yang, Z., Zhang, J., Xu, Y., Gao, X.: A geometry study on the capacity of wireless networks via percolation. IEEE Trans. Commun. 58(10), 2916–2925 (2010)CrossRefGoogle Scholar
  5. 5.
    Jain, K., Padhye, J., Padmanabhan, V.N., Qiu, L.: Impact of interference on multi-hop wireless network performance. Wirel. Netw. 11(4), 471–487 (2005)CrossRefGoogle Scholar
  6. 6.
    Keshavarz-Haddad, A., Ribeiro, V., Riedi, R.: Broadcast capacity in multihop wireless networks. In: Proceedings of the 12th Annual International Conference on Mobile Computing and Networking, pp. 239–250. ACM (2006)Google Scholar
  7. 7.
    Kodialam, M., Nandagopal, T.: Characterizing achievable rates in multi-hop wireless networks: the joint routing and scheduling problem. In: Proceedings of the 9th Annual International Conference on Mobile Computing and Networking, pp. 42–54. ACM (2003)Google Scholar
  8. 8.
    Kumar, V., Marathe, M.V., Parthasarathy, S., Srinivasan, A.: Algorithmic aspects of capacity in wireless networks. In: ACM SIGMETRICS Performance Evaluation Review, vol. 33, pp. 133–144. ACM (2005)Google Scholar
  9. 9.
    Li, X.Y.: Multicast capacity of wireless ad hoc networks. IEEE/ACM Trans. Networking (TON) 17(3), 950–961 (2009)CrossRefGoogle Scholar
  10. 10.
    Li, X.Y., Zhao, J., Wu, Y.W., Tang, S.J., Xu, X.H., Mao, X.F.: Broadcast capacity for wireless ad hoc networks. In: 5th IEEE International Conference on Mobile Ad Hoc and Sensor Systems, 2008. MASS 2008, pp. 114–123. IEEE (2008)Google Scholar
  11. 11.
    Lu, N., Shen, X.S.: Scaling laws for throughput capacity and delay in wireless networks—a survey. IEEE Commun. Surv. Tutorials 16(2), 642–657 (2014)CrossRefGoogle Scholar
  12. 12.
    Peraki, C., Servetto, S.D.: On the maximum stable throughput problem in random networks with directional antennas. In: Proceedings of the 4th ACM International Symposium on Mobile Ad Hoc Networking & Computing, pp. 76–87. ACM (2003)Google Scholar
  13. 13.
    Sadjadpour, H.R., Wang, Z., et al.: The capacity of wireless ad hoc networks with multi-packet reception. IEEE Trans. Commun. 58(2) (2010)CrossRefGoogle Scholar
  14. 14.
    Shakkottai, S., Liu, X., Srikant, R.: The multicast capacity of large multihop wireless networks. IEEE/ACM Trans. Networking (TON) 18(6), 1691–1700 (2010)CrossRefGoogle Scholar
  15. 15.
    Wan, P.J., Frieder, O., Jia, X., Yao, F., Xu, X., Tang, S.: Wireless Link Scheduling Under Physical Interference Model. IEEE (2011)Google Scholar
  16. 16.
    Wang, Z., Sadjadpour, H., Garcia-Luna-Aceves, J.J.: The capacity and energy efficiency of wireless ad hoc networks with multi-packet reception. In: Proceedings of the 9th ACM International Symposium on Mobile Ad Hoc Networking and Computing, pp. 179–188. ACM (2008)Google Scholar
  17. 17.
    Yi, S., Pei, Y., Kalyanaraman, S.: On the capacity improvement of ad hoc wireless networks using directional antennas. In: Proceedings of the 4th ACM International Symposium on Mobile Ad Hoc Networking & Computing, pp. 108–116. ACM (2003)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Computing Science and MathematicsUniversity of StirlingStirlingUK

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