Centre for Discrete and Applicable Mathematics

 CDAM Research Report, LSE-CDAM-2001-10

November 2001

Channel Assignment on Infinite Sets under Frequency-Distance Constraints

Jan van den Heuvel and Colin McDiarmid


This is the draft of a chapter in: S. Hurley and R.A.Leese, eds., "Models and Methods for Radio Channel Assignment", Oxford University Press, scheduled to appear in 2002.

This report describes work by the authors and others on mathematical approaches on channel assignment for transmitters positioned in the plane. We consider the situation that there are an infinite number of transmitters. The only constraints are binary channel separation constraints determined by the distance of two transmitters. Results for general sets (satisfying a mild density condition) are obtained when the re-use distance (the minimum distance that two transmitters need to have in order to be allowed to use the same frequency) is large. More precise answers for small distances are determined for sets with additional structure (in particular 2-dimensional lattices).

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