  In this article, we examine several design and complexity aspects of the
optimal physical layer resource allocation problem for a generic interference
channel (IC). The latter is a natural model for multi-user communication
networks. In particular, we characterize the computational complexity, the
convexity as well as the duality of the optimal resource allocation problem.
Moreover, we summarize various existing algorithms for resource allocation and
discuss their complexity and performance tradeoff. We also mention various open
research problems throughout the article.
