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To explore the advantages of software defined network (SDN), while preserving the legacy networking systems, a natural deployment strategy is to deploy a hybrid SDN incrementally to improve the network performance. In this paper, we address two technical challenges: an incremental deployment strategy and a throughput-maximization routing, for deploying a hybrid network incrementally. For incremental deployment, we propose a heuristic algorithm for deploying a hybrid SDN under the budget constraint, and prove the approximate factor of 1- 1/e. For throughput-maximization routing, we apply a depth-first-search method and a randomized rounding mechanism to solve the multi-commodity h-splittable flow routing problem in a hybrid SDN, where h ≥ 1. We also prove that our method has approximation ratio O(1/log N), where N is the number of links in a hybrid SDN. We then show, by both analysis and …