On The Span Of A Random Channel Assignment Problem

In the radio channel assignment problems considered here, we must assign a ‘channel’ from the set 1,2,... of positive integers to each of n transmitters, and we wish to minimise the span of channels used, subject to the assignment leading to an acceptable level of interference. A standard form of this problem is the ‘constraint matrix’ model. The simplest case of this model (the 0, 1 case) is essentially graph colouring. We consider here a random model for the next simplest case (with lengths 0, 1 or 2), and determine the asymptotic behaviour of the span of channels needed as n→∞. We find that there is a ‘phase change’ in this behaviour, depending on the probabilities for the different lengths.

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Correspondence to Colin McDiarmid.

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McDiarmid, C. On The Span Of A Random Channel Assignment Problem. Combinatorica 27, 183–203 (2007). https://doi.org/10.1007/s00493-007-0051-4

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Mathematics Subject Classification (2000):

  • 05C80
  • 90B15
  • 05C15