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Device-to-device (D2D) communications underlying cellular networks are a novel approach for providing IoT services, in which D2D communication links and cellular communication links share the same channels. Unfortunately, various kinds of devices are randomly distributed in cellular networks and potentially result in critical interferences. To solve the interference problem, we propose a novel greedy-based channel assignment algorithm in this paper. First, we construct a novel interference graph that describes the interferences between pairs of communication links when they simultaneously share the same channel. Then, a novel channel assignment algorithm is proposed to alleviate system interferences by greedily assigning the best channel to each communication link, which is simple and feasible to implement. Moreover, we convert the channel assignment problem into a robust graph coloring problem and search for a near-optimal solution to minimize the system interferences. Numerical results indicate that the proposed algorithm not only dramatically improves the network capacity but also enhances the fairness among devices.