Approximability of OFDMA Scheduling

In this paper, we study the complexity and approximability of the orthogonal frequency-division multiple access (OFDMA) scheduling problem with uniformly related communication channels. Our modelling approach for this problem follows numerous studies from the engineering sciences that are mostly concerned with the performance of heuristics for different variants of the problem. One is given n ≥ 1 terminals each coming with a demand di > 0 and m ≥ n communication channels each coming with a cost parameter pj > 0. The channels shall be assigned to the terminals in a way that each channel is mapped to at most one terminal and each terminal receives at least one channel. Additionally, each channel j needs to be assigned a communication rate rj > 0 such that the sum of the rates of the channels mapped to terminal i satisfies at least the demand di. Applying the formulas for the Shannon capacity, the energy requirement for channel j is assumed to be pj(2 rj − 1). The objective is to minimize the sum of the energy requirements over all channels. We prove that the problem is NP-hard and cannot be approximated with approximation factor α, unless P = NP, where α > 1 is any polynomial time computable function. We then consider a complementary problem setting in which one is given a threshold on the energy requirement and the objective is to maximize λ such that each terminal receives a rate of at least λdi. We show that this maximin version of the problem admits a PTAS if all demands are identical and a 1 2 -approximation for general demands.