# Traffic Engineering in SDN/OSPF Hybrid Network

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3 the problem. It has been proved that optimizing of weight setting is a NP-complete problem [2]. Our proposed model can be reduced to the weight optimization problem in [3] if all the traffic is split in a pre-defined manner, i.e, all traffic is split to the shortest path and none to the longer paths. So the complexity of the entire problem is easily proved to be NP-complete. Due to the space limitations, the detailed proof is omitted. IV. ALGORITHM FOR TRAFFIC ENGINEERING IN HYBRID NETWORK Given the NP-completeness of the problem, we resort to heuristic algorithms. In this section, we firstly introduce our novel algorithm called SOTE, which is a local search heuristic algorithm. Then we give a simple example to illustrate our algorithm in detail. A. A novel algorithm SOTE Fig. 1. A hybrid network scenario weight setting ω. U is the maximum link utilization of the network. We assume that the traffic matrix and the topology of the network are steady for a short period. The locations and number of the SDN nodes are fixed and are determined by the experiments in section V. By adjusting the weight setting matrix ω and the splitting ratio of the flows x i out the SDN nodes, we intend to minimize the maximum link utilization of the network, i.e., minimize U. We can formulate the problem as following. e In(c) minimize U f e (ω) = TM vt e In(t) v V t V (1) f e (ω)+tm ct = x e (ω) c CN,t V (2) v,t V e Out(c) g vt e (ω) UC(e) e A (3) ω Z (4) x e (ω) 0 e A (5) (1) denotes that the traffic demands are meet in the flow routing. (2) denotes that the flows flow into the node equals the flows that flow out of this node. (3) denotes that the total flows on a edge cannot exceed its capacity. (4)-(5) denote that the weights are integers and the flow on a link must be nonnegative. C. Problem Complexity When the weight setting is fixed, the problem boils down to a multi-commodity linear programming problem, which can be solved in polynomial time [16]. However, the weights are integers and undetermined, which adds up the complexity of Algorithm 1: SOTE Input: G =(V,A), CN, C, TM Output: U 1 Initial weight setting matrix W, U ; 2 currutil = floydwarshall (G, W, T M) ; 3 bestutil = currutil ; 4 currweights = W ; 5 bestweights = W ; 6 foreach iteration times increase by one do 7 currweights =neighbour search (G, W ); 8 currutil =Splitting ratio (currweights, CN, T M, C, V, A); 9 if currutil < bestutil then 10 bestutil = currutil ; 11 bestweights = currweights ; 12 U = bestutil ; Algorithm 1 is SOTE. At the core of the algorithm is the neighbour search function (line 7) and the Splitting ratio function (line 8). We first use Floyd algorithm to find the shortest paths between the two nodes and route the traffic demands to obtain the current link utilization (line 2). Then we set the current weight setting and link utilization to be the best weight setting and utilization (line 3-5 ). In each iteration of local search (line 6-11), we change the weights of the links (line 7). When we obtain a weight setting, we use the splitting ratio function to optimize the splitting ratio of the flows coming out the SDN nodes (line 8). We evaluate the maximum link utilization with the current weight setting and the optimized splitting ratio (line 9-11). We iterate to get the solution finally. Algorithm 2 shows when the weight setting is fixed, how to optimize the splitting ratio of the SDN nodes. We firstly construct Directed Acyclic Graphs (DAGs) for treating every node d as a destination node (line 2). DAG in the algorithm denotes the matrix that stores all possible paths between the 565

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