To the best of our knowledge, there have been very few work on computational algorithms for the core or its variants in MC-nets games. One exception is the work by [Hirayama, et.al., 2014], where a constraint generation algorithm has been proposed to compute a payoff vector belonging to the least core. In this paper, we generalize this algorithm into the one for finding a payoff vector belonging to ϵ-core with pre-specified bound guarantee. The underlying idea behind this algorithm is basically the same as the previous one, but one key contribution is to give a clearer view on the pricing problem leading to the development of our new general algorithm. We showed that this new algorithm was correct and never be trapped in an infinite loop. Furthermore, we empirically demonstrated that this algorithm really presented a trade-off between solution quality and computational costs on some benchmark instances.

This paper investigates data uploading in cellular networks with the consideration of device-to-device (D2D) communications. A generalized data uploading scheme is proposed by leveraging D2D cooperation among the devices to reduce the data uploading time. In this scheme, we extend the conventional schemes on cooperative D2D data uploading for cellular networks to a more general case, which considers D2D cooperation among both the devices with or without uploading data. To motivate D2D cooperation among all available devices, we organize the devices within communication range by offering them rewards to construct multi-hop D2D chains for data uploading. Specifically, we formulate the problem of chain formation among the devices for data uploading as a coalitional game. Based on merge-and-split rules, we develop a coalition formation algorithm to obtain the solution for the formulated coalitional game with convergence on a stable coalitional structure. Finally, extensive numerical results show the effectiveness of our proposed scheme in reducing the average data uploading time.