Performance limits for FDMA cellular systems described by hypergraphs

The authors present some preliminary material about hypergraphs, including a discussion of what they call random hypergraph multicolorings, a notion which is central to the analysis of frequency-assignment algorithms. They show that for any frequency-assignment algorithm, the carried traffic function must satisfy T(r)⩽T₀(r), where T₀(r) is a simple function that can be computed by linear programming. They give an asymptotic analysis of a class of `fixed´ frequency-assignment algorithms, and show that in the limit as n→∞, these algorithms achieve carried traffic functions that are at least as large as T<sub>1</sub>( r), another simple function that can be computed by linear programming. They show that T<sub>0</sub>(r)=T<sub>1</sub>(r). This common value, denoted by T<sub>H,p</sub>(r) is the function referred to above. They also describe some of the most important properties of the function T<sub>H,p</sub>(r), and identify the `most favorable´ traffic patterns for a given hypergraph H