Annals of Operations Research

, Volume 107, Issue 1–4, pp 143–159 | Cite as

Channel Assignment with Large Demands

  • Stefanie Gerke
  • Colin McDiarmid


We introduce a general static model for radio channel assignment, the ‘feasible assignments model’, in which to investigate the effects of changes in demand. For a fixed instance of this model where only the demands can vary, we consider the span of spectrum needed for a feasible assignment of channels to transmitters, and compare this span with a collection of lower bounds, in the limit when demands at the transmitters get large. We introduce a relevant measure which generalises the imperfection ratio of a graph and give alternative descriptions. We show that for a fixed instance of the feasible assignments model where only the demands can vary, on input the demands we can find the span in polynomial time. For the special case when the feasible assignments can be described by means of a complete graph together with co-site and adjacent constraints, we give a formula for the span. This yields clique-based lower bounds for the span in general problems.

channel assignment graph imperfection clique-bounds 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    A. Gamst, Some lower bounds for a class of frequency assignment problems, IEEE Transactions on Vehicular Technology VT-35(1) (1986) 8–14.Google Scholar
  2. [2]
    S. Gerke and C. McDiarmid, Graph imperfection, J. Combinatorial Theory B 83 (2001) 58–78.Google Scholar
  3. [3]
    S. Gerke and C. McDiarmid, Graph imperfection II, J. Combinatorial Theory B 83 (2001) 79–101.Google Scholar
  4. [4]
    S. Gerke and C. McDiarmid, Graph imperfection with a co-site constraint, Manuscript.Google Scholar
  5. [5]
    S. Hurley and R. Leese, eds., Models and Methods for Radio Channel Assignment (Oxford University Press) to appear.Google Scholar
  6. [6]
    M. Grötschel, L. Lovász and A. Schrijver, Geometric Algorithms and Combinatorial Optimization, 2nd ed. (Springer, 1993).Google Scholar
  7. [7]
    W.K. Hale, Frequency assignment: Theory and applications, in: Proceedings of the IEEE' 68 (1980) pp. 1497-1514.Google Scholar
  8. [8]
    C. McDiarmid, Channel assignment and discrete mathematics, in: Recent Advances in Theoretical and Applied Discrete Mathematics, eds. C. Linhares-Salas and B. Reed (Springer, 2002) to appear.Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Stefanie Gerke
    • 1
  • Colin McDiarmid
    • 2
  1. 1.TU München, Institut für InformatikMünchenGermany
  2. 2.Department of Statistics, 1University of OxfordOxfordUK

Personalised recommendations