Greedy online frequency allocation in cellular networks

The online frequency allocation problem for cellular networks has been well studied in these years. Given a mobile telephone network, whose geographical coverage area is divided into cells, phone calls are served by assigning frequencies to them, and no two calls emanating from the same or neighboring cells are assigned the same frequency. Assuming an online setting that the calls arrive one by one, the problem is to minimize the span of the frequencies used. In this paper, we study the greedy approach for the online frequency allocation problem, which assigns the minimal available frequency to a new call so that the call does not interfere with calls of the same cell or neighboring cells. If the calls have infinite duration, the competitive ratio of greedy algorithm has a tight upper bound of 17/7, which closes the gap of [17/17, 2.5) which was proved earlier. If the calls have finite duration, i.e., each call may be terminated at some time, the competitive ratio of the greedy algorithm has a tight upper bound of 3.