Bandwidth Constrained Multi-interface Networks

  • Gianlorenzo D’Angelo
  • Gabriele Di Stefano
  • Alfredo Navarra
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6543)


In heterogeneous networks, devices can communicate by means of multiple wired or wireless interfaces. By switching among interfaces or by combining the available interfaces, each device might establish several connections. A connection is established when the devices at its endpoints share at least one active interface. Each interface is assumed to require an activation cost, and provides a communication bandwidth. In this paper, we consider the problem of activating the cheapest set of interfaces among a network G = (V,E) in order to guarantee a minimum bandwidth B of communication between two specified nodes. Nodes V represent the devices, edges E represent the connections that can be established. In practical cases, a bounded number k of different interfaces among all the devices can be considered. Despite this assumption, the problem turns out to be NP-hard even for small values of k and Δ, where Δ is the maximum degree of the network. In particular, the problem is NP-hard for any fixed k ≥ 2 and Δ ≥ 3, while it is polynomially solvable when k = 1, or Δ ≤ 2 and k = O(1). Moreover, we show that the problem is not approximable within ηlogB or Ω(loglog|V|) for any fixed k ≥ 3, Δ ≥ 3, and for a certain constant η, unless \(P={\textit{NP}}\). We then provide an approximation algorithm with ratio guarantee of bmax, where bmax is the maximum communication bandwidth allowed among all the available interfaces. Finally, we focus on particular cases by providing complexity results and polynomial algorithms for Δ ≤ 2.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Ahuja, R., Magnanti, T., Orlin, J.: Network Flows: Theory, Algorithms, and Applications. Prentice-Hall, Englewood Cliffs (1993)MATHGoogle Scholar
  2. 2.
    Athanassopoulos, S., Caragiannis, I., Kaklamanis, C., Papaioannou, E.: Energy-efficient communication in multi-interface wireless networks. In: Královič, R., Niwiński, D. (eds.) MFCS 2009. LNCS, vol. 5734, pp. 102–111. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  3. 3.
    Bahl, P., Adya, A., Padhye, J., Walman, A.: Reconsidering wireless systems with multiple radios. SIGCOMM Comput. Commun. Rev. 34(5), 39–46 (2004)CrossRefGoogle Scholar
  4. 4.
    Caporuscio, M., Charlet, D., Issarny, V., Navarra, A.: Energetic Performance of Service-oriented Multi-radio Networks: Issues and Perspectives. In: 6th Int. Workshop on Software and Performance (WOSP), pp. 42–45. ACM Press, New York (2007)Google Scholar
  5. 5.
    Cavalcanti, D., Gossain, H., Agrawal, D.: Connectivity in multi-radio, multi-channel heterogeneous ad hoc networks. In: IEEE 16th Int. Symp. on Personal, Indoor and Mobile Radio Communications (PIMRC), pp. 1322–1326. IEEE, Los Alamitos (2005)Google Scholar
  6. 6.
    D’Angelo, G., Di Stefano, G., Navarra, A.: Minimizing the Maximum Duty for Connectivity in Multi-Interface Networks. In: Zhong, F. (ed.) COCOA 2010, Part II. LNCS, vol. 6509, pp. 254–267. Springer, Heidelberg (2010)Google Scholar
  7. 7.
    Draves, R., Padhye, J., Zill, B.: Routing in multi-radio, multi-hop wireless mesh networks. In: 10th Annual International Conference on Mobile Computing and Networking (MobiCom), pp. 114–128. ACM, New York (2004)Google Scholar
  8. 8.
    Faragó, A., Basagni, S.: The effect of multi-radio nodes on network connectivity—a graph theoretic analysis. In: IEEE Int. Workshop on Wireless Distributed Networks (WDM). IEEE, Los Alamitos (2008)Google Scholar
  9. 9.
    Garey, M.R., Johnson, D.S.: Computers and Intractability, A Guide to the Theory of NP-Completeness. W.H. Freeman and Company, New York (1979)MATHGoogle Scholar
  10. 10.
    Gens, G., Levner, E.: Computational complexity of approximation algorithms for combinatorial problems. In: Becvar, J. (ed.) MFCS 1979. LNCS, vol. 74, pp. 292–300. Springer, Heidelberg (1979)CrossRefGoogle Scholar
  11. 11.
    Görtz, S., Klose, A.: Analysis of some greedy algorithms for the single-sink fixed-charge transportation problem. Journal of Heuristics 15(4), 331–349 (2009)CrossRefMATHGoogle Scholar
  12. 12.
    Güntzer, M.M., Jungnickel, D.: Approximate minimization algorithms for the 0/1 Knapsack and Subset-Sum Problem. Operations Research Letters 26(2), 55–66 (2000)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Klasing, R., Kosowski, A., Navarra, A.: Cost Minimization in Wireless Networks with a Bounded and Unbounded Number of Interfaces. Networks 53(3), 266–275 (2009)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Kosowski, A., Navarra, A., Pinotti, M.C.: Exploiting Multi-Interface Networks: Connectivity and Cheapest Paths. Wireless Networks 16(4), 1063–1073 (2010)CrossRefGoogle Scholar
  15. 15.
    Lawer, E.: Combinatorial Optimization: Networks and Matroids. Holt, Rinehart, and Winston (1976)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Gianlorenzo D’Angelo
    • 1
  • Gabriele Di Stefano
    • 1
  • Alfredo Navarra
    • 2
  1. 1.Dipartimento di Ingegneria Elettrica e dell’InformazioneUniversità degli Studi dell’AquilaItaly
  2. 2.Dipartimento di Matematica e InformaticaUniversità degli Studi di PerugiaItaly

Personalised recommendations