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Maximum Matching in Multi-Interface Networks

  • Adrian Kosowski
  • Alfredo Navarra
  • Dominik Pajak
  • Cristina M. Pinotti
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7402)

Abstract

In heterogeneous networks, devices can communicate by means of multiple wireless interfaces. By choosing which interfaces to switch on at each device, several connections might be established. That is, the devices at the endpoints of each connection share at least one active interface.

In this paper, we consider the standard matching problem in the context of multi-interface wireless networks. The aim is to maximize the number of parallel connections without incurring in interferences. Given a network G = (V,E), nodes V represent the devices, edges E represent the connections that can be established. If node x participates in the communication with one of its neighbors by means of interface i, then another neighboring node of x can establish a connection (but not with x) only if it makes use of interface j ≠ i. The size of a solution for an instance of the outcoming matching problem, that we call Maximum Matching in Multi-Interface networks (3MI for short), is always in between the sizes of the solutions for the same instance with respect to the standard matching and its induced version problems. However, we prove that 3MI is NP-hard even for proper interval graphs and for bipartite graphs of maximum degree Δ ≥ 3. We also show polynomially solvable cases of 3MI with respect to different assumptions.

Keywords

Polynomial Time Algorithm Match Problem Interval Graph Maximum Match Complete Bipartite Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    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
  2. 2.
    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
  3. 3.
    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
  4. 4.
    Brandstädt, A., Mosca, R.: On distance-3 matchings and induced matchings. Discrete Applied Mathematics 159, 509–520 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Cameron, K.: Induced matching. Discrete Applied Mathematics 24, 97–102 (1989)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    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 (2007)Google Scholar
  7. 7.
    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 (2005)Google Scholar
  8. 8.
    D’Angelo, G., Di Stefano, G., Navarra, A.: Bandwidth Constrained Multi-interface Networks. In: Černá, I., Gyimóthy, T., Hromkovič, J., Jefferey, K., Králović, R., Vukolić, M., Wolf, S. (eds.) SOFSEM 2011. LNCS, vol. 6543, pp. 202–213. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  9. 9.
    D’Angelo, G., Stefano, G.D., Navarra, A.: Minimize the maximum duty in multi-interface networks. Algorithmica 63(1–2), 274–295 (2012)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    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 (2004)Google Scholar
  11. 11.
    Duckworth, W., Manlove, D., Zito, M.: On the approximability of the maximum induced matching problem. Journal of Discrete Algorithms 3, 79–91 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Edmonds, J.: Paths, trees and flowers. Journal of Mathematics 17, 449–467 (1965)MathSciNetzbMATHGoogle Scholar
  13. 13.
    Faragó, A., Basagni, S.: The effect of multi-radio nodes on network connectivity—a graph theoretic analysis. In: Proceedings of the IEEE International Workshop on Wireless Distributed Networks (WDM). IEEE (2008)Google Scholar
  14. 14.
    Gabow, H.N.: An efficient reduction technique for degree-constrained subgraph and bidirected network flow problems. In: Proceedings of the 15th Annual ACM Symposium on Theory of Computing (STOC), pp. 448–456. ACM (1983)Google Scholar
  15. 15.
    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
  16. 16.
    Golumbic, M.C., Lewenstein, M.: New results on induced matchings. Discrete Applied Mathematics 101, 157–165 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    Kang, R.J., Mnich, M., Müller, T.: Induced Matchings in Subcubic Planar Graphs. In: de Berg, M., Meyer, U. (eds.) ESA 2010. LNCS, vol. 6347, pp. 112–122. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  18. 18.
    Kanj, I., Pelsmajer, M.J., Schaefer, M., Xia, G.: On the induced matching problem. Journal on Computer System Science 77, 1058–1070 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    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)MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Kobler, D., Rotics, U.: Finding maximum induced matchings in subclasses of claw-free and p5-free graphs, and in graphs with matching and induced matching of equal maximum size. Algorithmica 37, 327–346 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  21. 21.
    Kosowski, A., Navarra, A., Pinotti, M.: Exploiting Multi-Interface Networks: Connectivity and Cheapest Paths. Wireless Networks 16(4), 1063–1073 (2010)CrossRefGoogle Scholar
  22. 22.
    Zito, M.: Induced Matchings in Regular Graphs and Trees. In: Widmayer, P., Neyer, G., Eidenbenz, S. (eds.) WG 1999. LNCS, vol. 1665, pp. 89–100. Springer, Heidelberg (1999)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Adrian Kosowski
    • 1
  • Alfredo Navarra
    • 2
  • Dominik Pajak
    • 1
  • Cristina M. Pinotti
    • 2
  1. 1.LaBRIINRIA Bordeaux Sud-ouestTalenceFrance
  2. 2.Dipartimento di Matematica e InformaticaUniversità degli Studi di PerugiaItaly

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