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The personal communication network (PCN) is an emerging wireless network that promises many new services for the telecommunication industry. The proliferation of demands for extending wireless services to integrated services which supports the transmission of data and multimedia information has resulted in the need for broadband wireless systems that are able to provide service capabilities similar to those of wireline networks. The ATM cell-relay paradigm is one possible approach to provide broadband wireless transmission with PCNs using the ATM switching networks for interconnection of PCN cells. In an ATM-based PCN, the communication path between a pair of mobile terminals might be elongated due to the mobility of the terminals. The link allocation problem is that of allocating backbone links among ATM switches to reduce the effects of terminal mobility on the performance of ATM-based PCNs. Huang and Wang (1997) have shown that this problem is NP-complete. In this paper, we propose a new efficient heuristic algorithm for the link allocation problem. One novel feature of our algorithm is that we are able to derive sufficient conditions under which our algorithm is able to guarantee optimal solutions. Our empirical study shows that the average lengths of communication paths obtained by our algorithm are shorter than those obtained by Huang and Wang's algorithm. In addition, the number of successfully established paths obtained by our algorithm is significantly more than that obtained by the aforementioned.