Computational complexity of some interference graph calculations (mobile radio)

The amount of work needed to generate the families of complete, maximal complete, independent, and maximal independent subsets of the interference graphs of mobile radio telephone networks is investigated. It is shown that the family of maximal complete subsets can always be computed, whereas, for complete sets, difficulties arise with larger reuse distances, and both the independent and maximal independent sets remain inaccessible except for networks with only little frequency reuse. It is shown that the size of the network is a limiting factor in the case of independent and maximal independent sets, since the number of members of these families always increases exponentially with the number of cells. On the other hand, the growth of the number of complete or maximal complete subsets with the size of the network is always linear.>