Advertisement

Connectivity in Multi-interface Networks

  • Adrian Kosowski
  • Alfredo Navarra
  • Cristina M. Pinotti
Conference paper
  • 177 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5474)

Abstract

Let G = (V,E) be a graph which models a set of wireless devices (nodes V) that can communicate by means of multiple radio interfaces, according to proximity and common interfaces (edges E). In general, every node holds a subset of all the possible k interfaces. Such networks are known as multi-interface networks. In this setting, we study a basic problem called Connectivity, corresponding to the well-known Minimum Spanning Tree problem in graph theory. In practice, we need to cover a subgraph of G of minimum cost which contains a spanning tree of G. A connection is covered (activated) when the endpoints of the corresponding edge share at least one active interface.

The connectivity problem turns out to be APX-hard in general and for many restricted graph classes, however it is possible to provide approximation algorithms: 2-approximation in general and \((2-\frac 1 k)\)-approximation for unit cost interfaces. We also consider the problem in special graph classes, such as graphs of bounded degree, planar graphs, graphs of bounded treewidth, complete graphs.

Keywords

Energy saving wireless network multi-interface network approximation algorithm 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    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
  2. 2.
    Draves, R., Padhye, J., Zill, B.: Routing in multi-radio, multi-hop wireless mesh networks. In: Proceedings of the 10th annual international conference on Mobile computing and networking (MobiCom), pp. 114–128. ACM, New York (2004)Google Scholar
  3. 3.
    Cavalcanti, D., Gossain, H., Agrawal, D.: Connectivity in multi-radio, multi-channel heterogeneous ad hoc networks. In: Proceedings of the IEEE 16th International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC), pp. 1322–1326. IEEE, Los Alamitos (2005)Google Scholar
  4. 4.
    Faragó, A., Basagni, S.: The effect of multi-radio nodes on network connectivity—a graph theoretic analysis. In: Proceedings of the IEEE 19th International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC). IEEE, Los Alamitos (to appear) (2008)Google Scholar
  5. 5.
    Caporuscio, M., Charlet, D., Issarny, V., Navarra, A.: Energetic Performance of Service-oriented Multi-radio Networks: Issues and Perspectives. In: Proceedings of the 6th International Workshop on Software and Performance (WOSP), pp. 42–45. ACM Press, New York (2007)Google Scholar
  6. 6.
    Klasing, R., Kosowski, A., Navarra, A.: Cost minimisation in multi-interface networks. In: Chahed, T., Tuffin, B. (eds.) NET-COOP 2007. LNCS, vol. 4465, pp. 276–285. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  7. 7.
    Klasing, R., Kosowski, A., Navarra, A.: Cost minimisation in wireless networks with bounded and unbounded number of interfaces. To appear in NetworksGoogle Scholar
  8. 8.
    Kosowski, A., Navarra, A.: Cost minimisation in unbounded multi-interface networks. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Wasniewski, J. (eds.) PPAM 2007. LNCS, vol. 4967, pp. 1039–1047. Springer, Heidelberg (2008)CrossRefGoogle 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)zbMATHGoogle Scholar
  10. 10.
    Garey, M.R., Johnson, D.S., Tarjan, R.E.: The planar hamiltonian circuit problem is NP-complete. SIAM J. Comput. 5(4), 704–714 (1976)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Brooks, R.L.: On coloring the nodes of a network. Proceedings of Cambridge Philosophical Society 37, 194–197 (1941)CrossRefzbMATHGoogle Scholar
  12. 12.
    Lovász, L.: Three short proofs in graph theory. J. Comb. Theory Series B 19, 269–271 (1975)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Bodlaender, H.L.: Dynamic programming on graphs with bounded treewidth. In: Lepistö, T., Salomaa, A. (eds.) ICALP 1988. LNCS, vol. 317, pp. 105–118. Springer, Heidelberg (1988)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Adrian Kosowski
    • 1
    • 2
  • Alfredo Navarra
    • 3
  • Cristina M. Pinotti
    • 3
  1. 1.LaBRI - Université Bordeaux 1TalenceFrance
  2. 2.Department of Algorithms and System ModelingGdańsk University of TechnologyGdańskPoland
  3. 3.Dipartimento di Matematica e InformaticaUniversità degli Studi di PerugiaPerugiaItaly

Personalised recommendations