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Software defined networking is a new paradigm that separates the control plane from the data plane. To provide high scalability and reduce the controller load in a large-scale software defined network (SDN), a natural way is to deploy a cluster of distributed controllers so as to cooperatively manage the network. However, since each controller just manages a set of the connected (or associated) switches and usually holds the information of these switches (and connected links), it may result in controller load imbalance and link load imbalance. Thus, both controller load and link load should be optimized to achieve better QoS in SDNs. To this end, this paper tries to answer the following question: how to perform both controller load balancing and link load balancing in an SDN? We formulate the load-balancing routing for both links and controllers (LBR-LC) problem in an SDN, and prove its NP-hardness. A rounding …