  Numerous communication networks are emerging to serve the various demands and
improve the quality of service. Heterogeneous users have different requirements
on quality metrics such as delay and service efficiency. Besides, the networks
are equipped with different types and amounts of resources, and how to
efficiently optimize the usage of such limited resources to serve more users is
the key issue for communication networks. One powerful mathematical
optimization mechanism to solve the above issue is column generation (CG),
which can deal with the optimization problems with complicating constraints and
block angular structures. In this paper, we first review the preliminaries of
CG. Further, the branch-and-price (BP) algorithm is elaborated, which is
designed by embedding CG into the branch-and-bound scheme to efficiently obtain
the optimal solution. The applications of CG and BP in various communication
networks are then provided, such as space-air-ground networks and
device-to-device networks. In short, our goal is to help readers refine the
applications of the CG optimization tool in terms of problem formulation and
solution. We also discuss the possible challenges and prospective directions
when applying CG in the communication networks.
