Subcarrier Allocation in Multiuser OFDM Systems: Complexity and Approximability

We consider a number of related problem formulations pertaining to adaptive subcarrier allocation in multiuser Orthogonal Frequency-Division Multiplexing (OFDM) systems, and prove that they are NP-hard. Thus there exist no known algorithms that can provide optimal solutions for all instances of these problems in polynomial time. We further prove that these problems are hard to approximate in polynomial time. Finally, we discuss qualitatively the settings under which worst case performance is likely to be observed.