Deterministic Online Call Control in Cellular Networks and Triangle-Free Cellular Networks

Wireless Communication Networks based on Frequency Division Multiplexing (FDM in short) plays an important role in the field of communications, in which each request can be satisfied by assigning a frequency. To avoid interference, each assigned frequency must be different to the neighboring assigned frequencies. Since frequency is a scarce resource, the main problem in wireless networks is how to utilize the frequency as fully as possible. In this paper, we consider the call control problem. Given a fixed bandwidth of frequencies and a sequence of communication requests, in handling each request, we must immediately choose an available frequency to accept (or reject) it. The objective of call control problem is to maximize the number of accepted requests. We study the asymptotic performance, i.e., the number of requests in the sequence and the number of available frequencies are very large positive integers. In this paper, we give a 7/3-competitive algorithm for call control problem in cellular network, improving the previous 2.5-competitive result. Moreover, we investigate the triangle-free cellular network, propose a 9/4-competitive algorithm and prove that the lower bound of competitive ratio is at least 5/3.