Abstract
A radiocommunication system has to satisfy the channel requests in its service area subject to the constraints that the number of channels is limited and co-channel interference must be excluded. This paper explores the possibility of finding optimal or nearly optimal channel assignments in polynomial time. It relates this problem to ‘graph-coloring’ and, if the network is assumed as cellular, to ‘packing in the plane’. An approximation algorithm is designed which satisfies at least a fraction of 1−e −1 of the maximum number of satisfiable requests. Several related versions of the problem are also analysed. For some of them, approximation schemes are discovered. Finally, NP-completeness is shown for a very restricted version and lower bounds for the best performance ratios are discussed (under the P≠NP-assumption).
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
R. J. Fowler, M. S. Paterson, and S. L. Tanimoto. Optimal packing and covering in the plane are NP-complete. Information Processing Lett., 12(3):133–137, June 1981.
M. R. Garey and D. S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H.Freeman and Company, San Francisco, 1979.
M. R. Garey, D. S. Johnson, and L. Stockmeyer. Some simplified NP-complete graph problems. Theor. Comput. Sci., 1(3):237–267, 1976.
F. Gavril. 1974. unpublished.
M. Grevel and A. Sachs. A graph theoretical analysis of dynamic channel assignment algorithms for mobile radiocommunication systems. Siemens Forsch. — u. Entwickl. — Ber., 12(5):298–305, 1983.
D. S. Hochbaum and W. Maass. Approximation schemes for covering and packing problems in image processing and VLSI. J. Assoc. Comput. Mach., 32(1):130–136, 1985.
D. S. Johnson. Approximation algorithms for combinatorial problems. J. Comp. System Sci., 9(3):256–278, 1974.
H. W. Lenstra, Jr. Integer Programming with a Fixed Number of Variables. Report 81-03, University of Amsterdam, Apr. 1981.
S. Sahni and T. Gonzales. P-complete approximation problems. J. Assoc. Comput. Mach., 23(3):555–565, 1976.
H. U. Simon. The Analysis of Dynamic and Hybrid Channel Assignment. SFB 124-B1 10/1988, Universität des Saarlandes, D-6600 Saarbrücken, FRG, May 1988.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1989 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Simon, H.U. (1989). Approximation algorithms for channel assignment in cellular radio networks. In: Csirik, J., Demetrovics, J., Gécseg, F. (eds) Fundamentals of Computation Theory. FCT 1989. Lecture Notes in Computer Science, vol 380. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51498-8_39
Download citation
DOI: https://doi.org/10.1007/3-540-51498-8_39
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-51498-5
Online ISBN: 978-3-540-48180-5
eBook Packages: Springer Book Archive