In this paper we consider communication issues arising in cellular (mobile) networks that utilize frequency division multiplexing (FDM) technology. In such networks, many users within the same geographical region can communicate simultaneously with other users of the network using distinct frequencies. The spectrum of available frequencies is limited; thus, efficient solutions to the frequency-allocation and the call-control problems are essential. In the frequency-allocation problem, given users that wish to communicate, the objective is to minimize the required spectrum of frequencies so that communication can be established without signal interference. The objective of the call-control problem is, given a spectrum of available frequencies and users that wish to communicate, to maximize the number of users served. We consider cellular, planar, and arbitrary network topologies.
In particular, we study the on-line version of both problems using competitive analysis. For frequency allocation in cellular networks, we improve the best known competitive ratio upper bound of 3 achieved by the folklore Fixed Allocation algorithm, by presenting an almost tight competitive analysis for the greedy algorithm; we prove that its competitive ratio is between 2.429 and 2.5 . For the call-control problem, we present the first randomized algorithm that beats the deterministic lower bound of 3 achieving a competitive ratio between 2.469 and 2.651 for cellular networks. Our analysis has interesting extensions to arbitrary networks. Also, using Yao's Minimax Principle, we prove two lower bounds of 1.857 and 2.086 on the competitive ratio of randomized call-control algorithms for cellular and arbitrary planar networks, respectively.