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1) We formulate an optimization problem to achieve the max- imum NCA with little upgrading cost. We prove that the problem is NP-hard, and give a heuristic algorithm to solve it with low complexity. Our scheme can achieve the minimum number of SDN switches to achieve the maximum NCA im- provement in a network [17,18].

2) We formulate the question that maximize energy saving with the fixed position of SDN switches deployed. We analyze the complexity of the question. Based on the deployment of SDN switches, we propose EPC to save more energy than other schemes by rerouting the flows.

3) The results of the evaluation show that our scheme can achieve 95% of the number of flows controlled with only 10% upgrading cost, and it also can achieve saving about 10% of the total power consumption when compared to the existing solutions.

The rest of the paper is organized as follows. In Section 2, we discuss some related works. In Section 3, we illustrate the motiva- tion and overview of the paper. Section 4 describes the issue and formulates it as an optimization issue. In Section 5, we prove that the problems are NP-hard, and also present a heuristic scheme to solve the questions. In Section 6, by comparing with the previous algorithms, our scheme can achieve better performance with few footprints. Section 7 concludes the paper.

2 Related Works

Some existing works propose deploying SDN switches to achieve network security, load balancing and traffic scheduling [9,19,20]. Dan Levin et al. [21] deploy SDN switches in enterprise networks using VLANs and switch ports to enable each flow to go through at least one SDN switch. The scheme is limited by the number of VLANs, and has a long path stretch. In [1], the objec- tive of the authors is to develop a SDN deployment scheme that can dynamically manage traffic in a network to accommodate dif- ferent traffic patterns. The solution has high complexity and is not feasible to use in backbone networks. Chu et al. [9] propose an approach to guarantee traffic reachability in the presence of any single link failure. By redirecting traffic on the failed link to SDN switches through pre-configured IP tunnels, the proposed approach can react quickly to the failures. With the help of coordination among SDN switches, it is able to explore multiple backup paths for traffic recovery. However, it increases the controller burden for complex pre-computed and wastes the flow table entries for pre- configured.

There have been a number of works focused on saving energy in traditional networks. The energy saving issues of OSPF protocol is studied in [13], where a novel network-level strategy is proposed to save energy based on a modification of current link-state rout- ing protocols, such as OSPF; according to this strategy, IP routers are able to power off some network links during low traffic pe- riods. But the solution in [13] is only a subset of router Shortest Path Trees (SPTs) that used to select the routing paths. In [4], the IP routers perform the shortest path routing using the distribute OSPF link weight optimization. While the SDN switches perform the multi-path routing with traffic flow splitting by the global SDN controller. They propose the scheme HEATE witch finds the opti- mal setting of OSPF link weight and splitting ratio of SDNs. Thus the traffic flow is aggregated onto partial links and the under uti- lized links can be turned off to save energy. Because [14] describe that after deciding on the values of the weights, a human opera- tor needs to change the IGP configuration on one or more routers, moreover, the scheme HEATE is based on [14] to develop the sys- tem. Thus, HEATE cannot run in the backbone environment.

In [3], the authors propose an energy-aware routing and re- source management model for large-scale networks based on SDN switches deployment. The controller of witch uses pre-established multi-paths (PMPs) and perform routing, admission control based on these paths. PMPs are turned on or off based on traffic conditions to save energy. However, they routing the flows by predefined fixed path that only connect ingress (IRs) with egress routers (ERs). So this path-based energy saving program is not flexible enough. In [22], Semu Tadesse et al. propose an effective way to achieve such a goal is to act on the backhaul network by control- ling the nodes operational state and the allocation of traffic flows. Their scheme, named EMMA, aims to both turn off idle nodes and concentrate traffic on the smallest possible set of links, which in its turn increases the number of idle nodes. In [23], B. Rawat et al. present various security threats that are resolved by SDN and new threats that arise as a result of SDN implementation. They also pro- vide a survey on the different strategies that are implemented to achieve energy efficiency and network security through SDN implementation.