The fast growth of machine-to-machine (M2M) communications in cellular networks brings the challenge of satisfying diverse Quality-of-Service (QoS) requirements of massive number of machine type communications (MTC) devices with limited radio resources. in this study we first introduce the minimum bandwidth resource allocation problem for M2M communications in 5G and beyond cellular networks. NP-hardness of the problem is proven. Then we propose a fast and efficient polynomial-time algorithm ...