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We extend the problem of optimizing user association for load balancing in cellular networks along 2-dimensions. First, we consider joint transmission, which is one of the coordinated multipoint techniques with which a user may be simultaneously served by multiple base stations. Second, we account for, mathematically, the coupling relation between the base stations' load levels that are dependent on each other due to inter-cell interference. We formulate two optimization problems, sum load minimization (MinSumL) and maximum load minimization (MinMaxL). We prove that both MinSumL and MinMaxL are NP-hard. We propose a mixed integer linear programming based scheme by means of linearization. This approach also leads to a bounding scheme for performance benchmarking. Then, we derive a set of partial optimality conditions. Fulfillment of the conditions will guarantee performance improvement for …