Advertisement

Exact Solution of a Class of Frequency Assignment Problems in Cellular Networks

(Extended Abstract)
  • Tiziana Calamoneri
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2841)

Abstract

The L(h, k)-labeling is an assignment of frequencies to the transmitters/receivers of a multihop radio network such that ‘close’transmitters must have frequencies which differ by at least k, and ‘very close’ transmitters must have frequencies which differ by at least h. The span of an L(h,k)-labeling is the difference between the largest and the smallest assigned frequency. In this paper we study the L(h, k)-labeling problem of cellular graphs, seeking those with minimum span for each value of k and hk.

Keywords

L(h&k)-labeling multihop radio networks frequency assignment problem cellular graphs 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aardal, K.I., van Hoesel, S.P.M., Koster, A.M.C.A., Mannino, C., Sassano, A.: Models and Solution Techniques for Frequency Assignment Problems. ZIB-Report 01-40, Konrad-Zuse-Zentrum fur Informationstechnik Berlin (2001)Google Scholar
  2. 2.
    Bertossi, A.A., Bonuccelli, M.A.: Code Assignment for Hidden Terminal Interference Avoidance in Multihop Packet Radio Networks. IEEE/ACM Trans. On Networking 3, 441–449 (1995)CrossRefGoogle Scholar
  3. 3.
    Bertossi, A.A., Pinotti, C.M., Tan, R.B.: Channel assignment with separation for interference avoidance in wireless networks. IEEE Transactions on Parallel and Distributed Systems (in press); Preliminary version in ACM Workshop DIAL M 2000 (2000)Google Scholar
  4. 4.
    Bodlaender, H.L., Kloks, T., Tan, R.B., van Leeuwen, J.: λ-Coloring of Graphs. In: Reichel, H., Tison, S. (eds.) STACS 2000. LNCS, vol. 1770, pp. 395–406. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  5. 5.
    Calamoneri, T., Petreschi, R.: L(2, 1)-Labeling of Planar Graphs (Extended Abstract). In: Proceedings of 5th ACM Int. Workshop on Discrete Algorithms and Methods for Mobile Computing and Communications (DIAL M), pp. 28–33 (2001)Google Scholar
  6. 6.
    Calamoneri, T., Petreschi, R.: On the Radiocoloring Problem. In: Das, S.K., Bhattacharya, S. (eds.) IWDC 2002. LNCS, vol. 2571, pp. 118–127. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  7. 7.
    Calamoneri, T., Petreschi, R.: λ-Coloring Unigraphs. In: Rajsbaum, S. (ed.) LATIN 2002. LNCS, vol. 2286, pp. 236–247. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  8. 8.
    Calamoneri, T., Pelc, A., Petreschi, R.: Labeling trees with a condition at distance two. In: Proceedings of R.C. Bose Centenary Symp. on Discr. Math. And Applications. electronic notes in discrete mathemathics (2002)Google Scholar
  9. 9.
    Calamoneri, T., Vocca, P.: On the Approximability of the L(h, k)-Labelling Problem (2003) (manuscript)Google Scholar
  10. 10.
    Chang, G.J., Kuo, D.: The L(2, 1)-labeling Problem on Graphs. SIAM J. Disc. Math. 9, 309–316 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Fotakis, D.A., Nikoletseas, S.E., Papadoulou, V.G., Spirakis, P.G.: NP-completeness Results and Efficient Approximations for Radiocoloring in Planar Graphs. In: Nielsen, M., Rovan, B. (eds.) MFCS 2000. LNCS, vol. 1893, p. 363. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  12. 12.
    Georges, J.P., Mauro, D.W.: Some results on λ j k-numbers of the products of complete graphs. Congr. Numer. 140, 141–160 (1999)zbMATHMathSciNetGoogle Scholar
  13. 13.
    Georges, J.P., Mauro, D.W., Stein, M.I.: Labeling products of complete graphs with a condition at distance two. SIAM J. Discr. Math. 14, 28–35 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Griggs, J.R., Yeh, R.K.: Labeling graphs with a Condition at Distance 2. SIAM J. Disc. Math. 5, 586–595 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    van den Heuvel, J., Leese, R.A., Shepherd, M.A.: Graph Labelling and Radio Channel Assignment. Journal of Graph Theory 29, 263–283 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Koster, A.M.C.A.: Frequency Assignment. Ph.D. thesis, Universiteit Maastricht (1999)Google Scholar
  17. 17.
    Liu, D., Yeh, R.K.: On distance two labelings of graphs. Ars Combinatoria 47, 13–22 (1997)zbMATHMathSciNetGoogle Scholar
  18. 18.
    Molloy, M., Salavatipour, M.R.: Frequency channel assignment on planar networks. In: Möhring, R.H., Raman, R. (eds.) ESA 2002. LNCS, vol. 2461, pp. 736–747. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  19. 19.
    Murphey, R.A., Pardalos, P.M., Resende, M.G.C.: Frequency Assignment Problems. In: Du, D.-Z., Pardalos, P.M. (eds.) Handbook of Combinatorial Optimization, pp. 295–377. Kluwer Academic Publishers, Dordrecht (1999)Google Scholar
  20. 20.
    Sakai, D.: Labeling Chordal Graphs: Distance Two Condition. SIAM J. Disc. Math. 7, 133–140 (1994)zbMATHCrossRefGoogle Scholar
  21. 21.
    Sen, A., Roxborough, T., Medidi, S.: Upper and Lower Bounds of a Class of Channel Assignmet Problems in Cellular Networks. IEEE INFOCOM 1998 (1998)Google Scholar
  22. 22.
    Shepherd, M.: Radio Channel Assignment. Ph.D. thesis, Merton College, Oxford (1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Tiziana Calamoneri
    • 1
  1. 1.Department of Computer ScienceUniversity of Rome “La Sapienza” – ItalyRomaItaly

Personalised recommendations