1 Coalition Formation towards Energy-Efficient Collaborative Mobile Computing Liyao Xiang 1 , Baochun Li 1 , and Bo Li 2 1 Department of Electrical and Computer Engineering, University of Toronto 2 Department of Computer Science, Hong Kong University of Science and Technology Abstract—With mobile offloading, computation-intensive tasks can be offloaded from mobile devices to the cloud to conserve energy. In principle, the idea is to trade the relatively low communication energy expense for high computation power con- sumption. In this paper, we propose that computation-intensive tasks can be distributed among nearby mobile devices, and focus on the case that a group of mobile users may collaborate with one another with one common target job. In particular, a user can reduce its own energy consumption by delegating a portion of the job to nearby users in a coalition. We propose distributed collaboration strategies based on game theory, and formulate the problem as a non-transferable utility coalition formation game in which users join or split from coalitions depending on the local preference. The stability of the resulting partition is studied. We show through simulations that our proposed algorithm reduces up to 22% of the average energy costs compared to the non- cooperative case, and the running time scales well as the number of users grows. I. I NTRODUCTION It is increasingly common for users with mobile devices to depend on the assistance from the cloud for their computation- intensive tasks. Cyber foraging and cloudlets [1] have long been proposed as a way to liberate mobile devices from severe resource constraints. Existing works have largely focused on migrating computation to the cloud, but new features such as Continuity in Mac OS X and WatchKit in iOS have made it possible to offload tasks to nearby devices via Bluetooth Low Energy. For example, a user with an Apple Watch can easily offload an unfinished email from her watch to her iPhone. Indeed, recent works (e.g., [2]) in the literature have pro- posed that the computational resources of a collection of collaborative mobile devices can be pooled for more efficient energy consumption. This clearly points out a trend that more and more mobile applications are designed to be executed in a distributed fashion, in collaboration with nearby devices that the same group of users owns. In fact, new research areas such as social sensing and crowdsourcing require the ability to recruit more than one mobile device to jointly work as a group. In previous works [2]–[7], mobile devices cooperate for the purpose of conserving energy or speeding up computation, under the assumption that the users are highly collaborative. However, mobile users are not altruistic in real life, rarely contributing freely to one another; typically, they tend to exchange computation results only with the collaborating users they choose, in order to reduce the workload on their own devices. Different from the previous work, we focus on how collaborating users are to be selected by each mobile user, where the goal is to minimize the energy cost. The intuitive optimal solution is to have everyone play the best strategy responses where each of them maximizes its own interest by acting according to the others’ actions, but this scheme takes too many iterations before converging to an agreement. We thus consider an alternative way that multiple coalitions for collaboration are formed, and each user can choose its collaborators by leaving or joining a coalition. In particular, we focus on the problem of how multiple coalitions are to be formed among a group of mobile users to reduce the average energy cost. We assume that as soon as a mobile user decides to form a coalition with other users, it enters a binding agreement with the other users within the coalition, and considers the benefit of the coalition as a whole. All users are cooperative and individually rational. With this assumption in place, we study the problem of how mobile users that are located in proximity to one another can form coalitions to complete a common computation-intensive job, with the objective of minimizing the energy consumption. The key questions to ask are: given a job partitioned into several tasks, how do heterogenous mobile users form coali- tions? Within each coalition, how do we distribute the tasks to each user? We assume that users are only concerned about the energy used for computation and network connections, in that the two constitute a major part of the energy consumption on a mobile device. The variability in energy characteristics of different devices and network connections should also be taken into consideration when allocating tasks. If we describe the computation capability and network connections of each mobile device by a resource graph, our problem can be formulated as an optimization problem over all partitions of the graph. However, seeking a centralized solution to minimize the overall energy cost is tricky and impractical. To address this problem, our contributions in this paper are two-fold. First, we formulated the task distribution problem as a 0-1 integer quadratic programming problem to determine the assignment of tasks to devices, in order to minimize the overall energy costs. By assuming a central arbitrator exists, we are able to obtain an optimal partition of the resource graph, as well as an optimal task assignment within each partition. Second, we proposed a distributed coalition formation algorithm for multiple mobile users, who are self- organized into disjoint independent coalitions.